[{"corr_author":"1","article_type":"original","quality_controlled":"1","file":[{"content_type":"application/pdf","creator":"dernst","file_id":"21004","file_size":235238,"checksum":"3b05bd625c81d038259a14f7e2ddd57c","relation":"main_file","date_created":"2026-01-19T08:19:46Z","success":1,"date_updated":"2026-01-19T08:19:46Z","access_level":"open_access","file_name":"2026_JourLondonMathSoc_Browning.pdf"}],"author":[{"last_name":"Browning","full_name":"Browning, Timothy D","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2026-01-19T08:23:15Z","_id":"21002","OA_place":"publisher","file_date_updated":"2026-01-19T08:19:46Z","scopus_import":"1","year":"2026","abstract":[{"text":"The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.","lang":"eng"}],"publication":"Journal of the London Mathematical Society","month":"01","department":[{"_id":"TiBr"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"title":"The Davenport–Heilbronn method: 80 years on","doi":"10.1112/jlms.70371","date_published":"2026-01-06T00:00:00Z","oa_version":"Published Version","issue":"1","PlanS_conform":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"06","intvolume":"       113","ddc":["510"],"project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"}],"date_created":"2026-01-18T23:02:44Z","has_accepted_license":"1","acknowledgement":"The author is very grateful to Jörg Brüdern, Simon Rydin Myerson and Trevor Wooley for their help and advice with preparing this survey, in addition to Vinay Kumaraswamy, Victor Wang and the anonymous referee for useful comments on an earlier draft. This work was supported by a FWF Grant (DOI 10.55776/P36278).\r\nOpen Access funding provided by Institute of Science and Technology Austria/KEMÖ.","article_processing_charge":"Yes (via OA deal)","publisher":"Wiley","type":"journal_article","volume":113,"publication_status":"published","language":[{"iso":"eng"}],"citation":{"mla":"Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” <i>Journal of the London Mathematical Society</i>, vol. 113, no. 1, e70371, Wiley, 2026, doi:<a href=\"https://doi.org/10.1112/jlms.70371\">10.1112/jlms.70371</a>.","chicago":"Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” <i>Journal of the London Mathematical Society</i>. Wiley, 2026. <a href=\"https://doi.org/10.1112/jlms.70371\">https://doi.org/10.1112/jlms.70371</a>.","apa":"Browning, T. D. (2026). The Davenport–Heilbronn method: 80 years on. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.70371\">https://doi.org/10.1112/jlms.70371</a>","ista":"Browning TD. 2026. The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. 113(1), e70371.","ama":"Browning TD. The Davenport–Heilbronn method: 80 years on. <i>Journal of the London Mathematical Society</i>. 2026;113(1). doi:<a href=\"https://doi.org/10.1112/jlms.70371\">10.1112/jlms.70371</a>","short":"T.D. Browning, Journal of the London Mathematical Society 113 (2026).","ieee":"T. D. Browning, “The Davenport–Heilbronn method: 80 years on,” <i>Journal of the London Mathematical Society</i>, vol. 113, no. 1. Wiley, 2026."},"article_number":"e70371","oa":1,"OA_type":"hybrid"},{"intvolume":"       340","type":"journal_article","volume":340,"article_processing_charge":"No","publisher":"Mathematical Sciences Publishers","date_created":"2026-02-16T15:17:27Z","citation":{"ieee":"N. Rome and S. Yamagishi, “Integral solutions to systems of diagonal equations,” <i>Pacific Journal of Mathematics</i>, vol. 340, no. 1. Mathematical Sciences Publishers, pp. 179–198, 2026.","ama":"Rome N, Yamagishi S. Integral solutions to systems of diagonal equations. <i>Pacific Journal of Mathematics</i>. 2026;340(1):179-198. doi:<a href=\"https://doi.org/10.2140/pjm.2026.340.179\">10.2140/pjm.2026.340.179</a>","short":"N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198.","mla":"Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” <i>Pacific Journal of Mathematics</i>, vol. 340, no. 1, Mathematical Sciences Publishers, 2026, pp. 179–98, doi:<a href=\"https://doi.org/10.2140/pjm.2026.340.179\">10.2140/pjm.2026.340.179</a>.","apa":"Rome, N., &#38; Yamagishi, S. (2026). Integral solutions to systems of diagonal equations. <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pjm.2026.340.179\">https://doi.org/10.2140/pjm.2026.340.179</a>","chicago":"Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” <i>Pacific Journal of Mathematics</i>. Mathematical Sciences Publishers, 2026. <a href=\"https://doi.org/10.2140/pjm.2026.340.179\">https://doi.org/10.2140/pjm.2026.340.179</a>.","ista":"Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 340(1), 179–198."},"arxiv":1,"publication_status":"published","language":[{"iso":"eng"}],"page":"179-198","OA_type":"green","oa":1,"external_id":{"arxiv":["2406.09256"]},"date_updated":"2026-02-17T11:43:14Z","article_type":"original","quality_controlled":"1","author":[{"full_name":"Rome, Nick","first_name":"Nick","last_name":"Rome"},{"id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","full_name":"Yamagishi, Shuntaro","first_name":"Shuntaro","last_name":"Yamagishi"}],"department":[{"_id":"TiBr"}],"abstract":[{"text":"We obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We improve the required number of variables compared to previous results by incorporating recent progress on Waring’s problem and the resolution of the main conjecture in Vinogradov’s mean value theorem.","lang":"eng"}],"publication":"Pacific Journal of Mathematics","month":"01","year":"2026","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2406.09256"}],"_id":"21242","OA_place":"repository","title":"Integral solutions to systems of diagonal equations","publication_identifier":{"issn":["0030-8730"],"eissn":["1945-5844"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","day":"01","issue":"1","oa_version":"Preprint","doi":"10.2140/pjm.2026.340.179","date_published":"2026-01-01T00:00:00Z"},{"date_updated":"2026-03-02T14:05:47Z","author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","orcid":"0000-0002-0704-7026","full_name":"Wang, Victor","first_name":"Victor","last_name":"Wang"},{"last_name":"Xu","full_name":"Xu, Max","first_name":"Max"}],"quality_controlled":"1","article_type":"original","corr_author":"1","department":[{"_id":"TiBr"}],"publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics","month":"01","abstract":[{"lang":"eng","text":"We prove that the average size of a mixed character sum (math. formular) (for a suitable smooth function w) is on the order of √x for all irrational real θ satisfying a weak Diophantine condition, where χ is drawn from the family of Dirichlet characters modulo a large prime r and where x 6 r. In contrast, it was proved by Harper that the average size is o(√x) for rational θ. Certain quadratic Diophantine equations play a key role in the present paper. "}],"year":"2026","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/prm.2026.10123"}],"_id":"21385","OA_place":"publisher","title":"Average sizes of mixed character sums","publication_identifier":{"eissn":["1473-7124"],"issn":["0308-2105"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","PlanS_conform":"1","oa_version":"Published Version","date_published":"2026-01-01T00:00:00Z","doi":"10.1017/prm.2026.10123","ddc":["510"],"project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"ec_funded":1,"type":"journal_article","article_processing_charge":"Yes (via OA deal)","publisher":"Cambridge University Press","acknowledgement":"We thank Ofir Gorodetsky, Andrew Granville, Adam Harper, Youness Lamzouri,\r\nKannan Soundararajan, Ping Xi, and Matt Young for their interest, helpful discussions, and comments. Special thanks are due to Jonathan Bober, Oleksiy Klurman,\r\nand Besfort Shala for sending us a letter about Question 1.3, and to Hung Bui\r\nfor informing us of [7]. V.W. thanks Stanford University for its hospitality and is supported by the European Union’s Horizon 2020 research and innovation program\r\nunder the Marie Skłodowska–Curie Grant Agreement No. 101034413. M.X. is supported by a Simons Junior Fellowship from the Simons Society of Fellows at the\r\nSimons Foundation.","has_accepted_license":"1","date_created":"2026-03-02T10:09:23Z","citation":{"short":"V. Wang, M. Xu, Proceedings of the Royal Society of Edinburgh: Section A Mathematics (2026) 1–15.","ama":"Wang V, Xu M. Average sizes of mixed character sums. <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>. 2026:1-15. doi:<a href=\"https://doi.org/10.1017/prm.2026.10123\">10.1017/prm.2026.10123</a>","ieee":"V. Wang and M. Xu, “Average sizes of mixed character sums,” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>. Cambridge University Press, pp. 1–15, 2026.","ista":"Wang V, Xu M. 2026. Average sizes of mixed character sums. Proceedings of the Royal Society of Edinburgh: Section A Mathematics., 1–15.","chicago":"Wang, Victor, and Max Xu. “Average Sizes of Mixed Character Sums.” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>. Cambridge University Press, 2026. <a href=\"https://doi.org/10.1017/prm.2026.10123\">https://doi.org/10.1017/prm.2026.10123</a>.","mla":"Wang, Victor, and Max Xu. “Average Sizes of Mixed Character Sums.” <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>, Cambridge University Press, 2026, pp. 1–15, doi:<a href=\"https://doi.org/10.1017/prm.2026.10123\">10.1017/prm.2026.10123</a>.","apa":"Wang, V., &#38; Xu, M. (2026). Average sizes of mixed character sums. <i>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/prm.2026.10123\">https://doi.org/10.1017/prm.2026.10123</a>"},"arxiv":1,"language":[{"iso":"eng"}],"publication_status":"epub_ahead","OA_type":"hybrid","page":"1-15","oa":1,"external_id":{"arxiv":["2411.14181"]}},{"publication_status":"published","language":[{"iso":"eng"}],"arxiv":1,"citation":{"ieee":"J. Glas and L. Hochfilzer, “On a question of Davenport and diagonal cubic forms over Fq(t),” <i>Mathematische Annalen</i>, vol. 391. Springer Nature, pp. 5485–5533, 2025.","short":"J. Glas, L. Hochfilzer, Mathematische Annalen 391 (2025) 5485–5533.","ama":"Glas J, Hochfilzer L. On a question of Davenport and diagonal cubic forms over Fq(t). <i>Mathematische Annalen</i>. 2025;391:5485-5533. doi:<a href=\"https://doi.org/10.1007/s00208-024-03035-z\">10.1007/s00208-024-03035-z</a>","ista":"Glas J, Hochfilzer L. 2025. On a question of Davenport and diagonal cubic forms over Fq(t). Mathematische Annalen. 391, 5485–5533.","chicago":"Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” <i>Mathematische Annalen</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00208-024-03035-z\">https://doi.org/10.1007/s00208-024-03035-z</a>.","apa":"Glas, J., &#38; Hochfilzer, L. (2025). On a question of Davenport and diagonal cubic forms over Fq(t). <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-024-03035-z\">https://doi.org/10.1007/s00208-024-03035-z</a>","mla":"Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” <i>Mathematische Annalen</i>, vol. 391, Springer Nature, 2025, pp. 5485–533, doi:<a href=\"https://doi.org/10.1007/s00208-024-03035-z\">10.1007/s00208-024-03035-z</a>."},"isi":1,"external_id":{"arxiv":["2208.05422"],"isi":["001376740400001"]},"oa":1,"OA_type":"hybrid","page":"5485-5533","ddc":["510"],"intvolume":"       391","date_created":"2024-12-22T23:01:48Z","has_accepted_license":"1","publisher":"Springer Nature","volume":391,"article_processing_charge":"Yes (via OA deal)","type":"journal_article","acknowledgement":"Open Access funding enabled and organized by Projekt DEAL.\r\nThe authors would like to thank Tim Browning for suggesting this project. Further they are grateful for his and Damaris Schindler’s helpful comments. We would also like to thank Efthymios Sofos for bringing Davenport’s question to our attention and Keith Matthews for providing us with scanned copies of the original correspondence. Finally we would like to thank the reviewer for helpful comments.","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"title":"On a question of Davenport and diagonal cubic forms over Fq(t)","date_published":"2025-04-01T00:00:00Z","doi":"10.1007/s00208-024-03035-z","oa_version":"Published Version","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","corr_author":"1","author":[{"last_name":"Glas","first_name":"Jakob","full_name":"Glas, Jakob","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb"},{"full_name":"Hochfilzer, Leonhard","first_name":"Leonhard","last_name":"Hochfilzer"}],"quality_controlled":"1","article_type":"original","file":[{"file_name":"2025_MathAnnalen_Glas.pdf","access_level":"open_access","date_updated":"2025-04-16T09:38:55Z","success":1,"checksum":"dcf57a8b01332c36e0cf2b0d1aeecb36","relation":"main_file","date_created":"2025-04-16T09:38:55Z","file_id":"19579","content_type":"application/pdf","creator":"dernst","file_size":650021}],"date_updated":"2025-05-19T14:04:46Z","_id":"18705","OA_place":"publisher","year":"2025","file_date_updated":"2025-04-16T09:38:55Z","scopus_import":"1","publication":"Mathematische Annalen","month":"04","abstract":[{"text":"Given a non-singular diagonal cubic hypersurface X⊂Pn−1 over Fq(t) with char(Fq)≠3, we show that the number of rational points of height at most |P| is O(|P|3+ε) for n=6 and O(|P|2+ε) for n=4. In fact, if n=4 and char(Fq)>3 we prove that the number of rational points away from any rational line contained in X is bounded by O(|P|3/2+ε). From the result in 6 variables we deduce weak approximation for diagonal cubic hypersurfaces for n≥7 over Fq(t) when char(Fq)>3 and handle Waring's problem for cubes in 7 variables over Fq(t) when char(Fq)≠3. Our results answer a question of Davenport regarding the number of solutions of bounded height to x31+x32+x33=x34+x35+x36 with xi∈Fq[t].","lang":"eng"}],"department":[{"_id":"TiBr"}],"related_material":{"record":[{"id":"18293","status":"public","relation":"earlier_version"}]}},{"acknowledgement":"Silverman, and Paul Voutier for the comments on the earlier version of this paper. The first author acknowledges the support by Dioscuri programme initiated by the Max Planck Society, jointly managed with the National Science Centre (Poland), and mutually funded by the Polish Ministry of Science and Higher Education and the German Federal Ministry of Education and Research. The second author has been supported by MIUR (Italy) through PRIN 2017 ‘Geometric, algebraic and analytic methods in arithmetic’ and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","type":"journal_article","publisher":"Cambridge University Press","volume":155,"article_processing_charge":"Yes (via OA deal)","ec_funded":1,"has_accepted_license":"1","date_created":"2023-01-16T11:45:22Z","intvolume":"       155","ddc":["510"],"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"page":"1646-1660","OA_type":"hybrid","keyword":["Elliptic curves","Néron models","division polynomials","height functions","discrete valuation rings"],"isi":1,"external_id":{"isi":["001174907100001"],"arxiv":["2203.02015"]},"oa":1,"arxiv":1,"citation":{"ieee":"B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5. Cambridge University Press, pp. 1646–1660, 2025.","ama":"Naskręcki B, Verzobio M. Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. 2025;155(5):1646-1660. doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>","short":"B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 155 (2025) 1646–1660.","apa":"Naskręcki, B., &#38; Verzobio, M. (2025). Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>","mla":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>.","chicago":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>.","ista":"Naskręcki B, Verzobio M. 2025. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 155(5), 1646–1660."},"language":[{"iso":"eng"}],"publication_status":"published","abstract":[{"lang":"eng","text":"In this note, we prove a formula for the cancellation exponent  kv,n between division polynomials  ψn  and  ϕn  associated with a sequence  {nP}n∈N of points on an elliptic curve  E  defined over a discrete valuation field  K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields."}],"publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","month":"10","department":[{"_id":"TiBr"}],"_id":"12311","OA_place":"publisher","scopus_import":"1","file_date_updated":"2025-12-30T06:45:47Z","year":"2025","quality_controlled":"1","article_type":"original","file":[{"date_updated":"2025-12-30T06:45:47Z","access_level":"open_access","file_name":"2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf","file_size":477624,"file_id":"20878","creator":"dernst","content_type":"application/pdf","date_created":"2025-12-30T06:45:47Z","relation":"main_file","checksum":"c5ec6e29aca2fb4533cb95fac409a0b2","success":1}],"author":[{"first_name":"Bartosz","full_name":"Naskręcki, Bartosz","last_name":"Naskręcki"},{"last_name":"Verzobio","full_name":"Verzobio, Matteo","first_name":"Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"date_updated":"2025-12-30T06:46:17Z","corr_author":"1","issue":"5","PlanS_conform":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","doi":"10.1017/prm.2024.7","date_published":"2025-10-01T00:00:00Z","oa_version":"Published Version","publication_identifier":{"issn":["0308-2105"],"eissn":["1473-7124"]},"title":"Common valuations of division polynomials","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"has_accepted_license":"1","date_created":"2025-08-24T22:01:31Z","article_processing_charge":"Yes (via OA deal)","type":"journal_article","publisher":"Oxford University Press","ec_funded":1,"volume":2025,"acknowledgement":"While working on this paper, the author was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. The author is very grateful to Tim Browning for suggesting the problem and for many useful discussions. We thank the anonymous referees for their many helpful comments, which improved the exposition of the paper. We are also grateful to Gal Binyamini for their interest in this work and for drawing our attention to the aforementioned paper [1].\r\nWe shared an early version of this paper with Per Salberger, who mentioned that he announced a new bound for smooth threefolds in P4 during a talk in 2019 (see [7] for the abstract). This result has not been published.","ddc":["510"],"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020"}],"intvolume":"      2025","isi":1,"external_id":{"isi":["001549126000001"],"arxiv":["2503.19451"]},"oa":1,"article_number":"rnaf249","OA_type":"hybrid","publication_status":"published","language":[{"iso":"eng"}],"arxiv":1,"citation":{"ista":"Verzobio M. 2025. Counting rational points on smooth hypersurfaces with high degree. International Mathematics Research Notices. 2025(16), rnaf249.","mla":"Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High Degree.” <i>International Mathematics Research Notices</i>, vol. 2025, no. 16, rnaf249, Oxford University Press, 2025, doi:<a href=\"https://doi.org/10.1093/imrn/rnaf249\">10.1093/imrn/rnaf249</a>.","apa":"Verzobio, M. (2025). Counting rational points on smooth hypersurfaces with high degree. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnaf249\">https://doi.org/10.1093/imrn/rnaf249</a>","chicago":"Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High Degree.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2025. <a href=\"https://doi.org/10.1093/imrn/rnaf249\">https://doi.org/10.1093/imrn/rnaf249</a>.","short":"M. Verzobio, International Mathematics Research Notices 2025 (2025).","ama":"Verzobio M. Counting rational points on smooth hypersurfaces with high degree. <i>International Mathematics Research Notices</i>. 2025;2025(16). doi:<a href=\"https://doi.org/10.1093/imrn/rnaf249\">10.1093/imrn/rnaf249</a>","ieee":"M. Verzobio, “Counting rational points on smooth hypersurfaces with high degree,” <i>International Mathematics Research Notices</i>, vol. 2025, no. 16. Oxford University Press, 2025."},"OA_place":"publisher","_id":"20222","year":"2025","scopus_import":"1","file_date_updated":"2025-09-02T07:55:05Z","publication":"International Mathematics Research Notices","month":"08","abstract":[{"lang":"eng","text":"Let X be a smooth projective hypersurface defined over Q. We provide new bounds for rational points of bounded height on X. In particular, we show that if X is a smooth projective hypersurface in Pn with n  4 and degree d  50, then the set of rational points on X of height bounded by B have cardinality On,d,ε (Bn−2+ε ). If X is smooth and has degree d  6, we improve the dimension growth conjecture bound. We achieve an analogue result for affine hypersurfaces whose projective closure is smooth."}],"department":[{"_id":"TiBr"}],"corr_author":"1","author":[{"orcid":"0000-0002-0854-0306","first_name":"Matteo","full_name":"Verzobio, Matteo","last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"file":[{"date_created":"2025-09-02T07:55:05Z","relation":"main_file","checksum":"482ae2be98841ee446cf2bdfcd79f86f","success":1,"file_size":540263,"creator":"dernst","file_id":"20275","content_type":"application/pdf","file_name":"2025_IMRN_Verzobio.pdf","date_updated":"2025-09-02T07:55:05Z","access_level":"open_access"}],"article_type":"original","quality_controlled":"1","date_updated":"2025-09-30T14:26:34Z","date_published":"2025-08-01T00:00:00Z","doi":"10.1093/imrn/rnaf249","oa_version":"Published Version","issue":"16","day":"01","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"title":"Counting rational points on smooth hypersurfaces with high degree"},{"publication_status":"published","language":[{"iso":"eng"}],"arxiv":1,"citation":{"ama":"Browning TD, Wilsch FA. Integral points on cubic surfaces: heuristics and numerics. <i>Selecta Mathematica New Series</i>. 2025;31(4). doi:<a href=\"https://doi.org/10.1007/s00029-025-01074-1\">10.1007/s00029-025-01074-1</a>","short":"T.D. Browning, F.A. Wilsch, Selecta Mathematica New Series 31 (2025).","ieee":"T. D. Browning and F. A. Wilsch, “Integral points on cubic surfaces: heuristics and numerics,” <i>Selecta Mathematica New Series</i>, vol. 31, no. 4. Springer Nature, 2025.","chicago":"Browning, Timothy D, and Florian Alexander Wilsch. “Integral Points on Cubic Surfaces: Heuristics and Numerics.” <i>Selecta Mathematica New Series</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00029-025-01074-1\">https://doi.org/10.1007/s00029-025-01074-1</a>.","mla":"Browning, Timothy D., and Florian Alexander Wilsch. “Integral Points on Cubic Surfaces: Heuristics and Numerics.” <i>Selecta Mathematica New Series</i>, vol. 31, no. 4, 81, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00029-025-01074-1\">10.1007/s00029-025-01074-1</a>.","apa":"Browning, T. D., &#38; Wilsch, F. A. (2025). Integral points on cubic surfaces: heuristics and numerics. <i>Selecta Mathematica New Series</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00029-025-01074-1\">https://doi.org/10.1007/s00029-025-01074-1</a>","ista":"Browning TD, Wilsch FA. 2025. Integral points on cubic surfaces: heuristics and numerics. Selecta Mathematica New Series. 31(4), 81."},"isi":1,"external_id":{"arxiv":["2407.16315"],"isi":["001552779800001"]},"oa":1,"article_number":"81","OA_type":"hybrid","ddc":["500"],"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","call_identifier":"FWF","grant_number":"P32428"},{"grant_number":"P36278","name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"}],"intvolume":"        31","has_accepted_license":"1","date_created":"2025-08-31T22:01:31Z","publisher":"Springer Nature","type":"journal_article","volume":31,"article_processing_charge":"Yes (via OA deal)","acknowledgement":"The authors owe a debt of thanks to Yonatan Harpaz for asking about circle method heuristics for log K3 surfaces. His contribution to the resulting discussion is gratefully acknowledged. Thanks are also due to Andrew Sutherland for help with numerical data for the equation x^3 + y^3 + z^3 = 1, together with Alex Gamburd, Amit Ghosh, Peter Sarnak and Matteo Verzobio for their interest in this paper. Special thanks are due to Victor Wang for helpful conversations about the circle method heuristics and to the anonymous referee for several useful comments. While working on this paper, the authors were supported by a FWF grant (DOI 10.55776/P32428), and the first author was supported by a further FWF grant (DOI 10.55776/P36278) and a grant from the School of Mathematics at the Institute for Advanced Study in Princeton.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"eissn":["1420-9020"],"issn":["1022-1824"]},"title":"Integral points on cubic surfaces: heuristics and numerics","date_published":"2025-09-01T00:00:00Z","doi":"10.1007/s00029-025-01074-1","oa_version":"Published Version","PlanS_conform":"1","issue":"4","day":"01","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","author":[{"first_name":"Timothy D","full_name":"Browning, Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","full_name":"Wilsch, Florian Alexander","first_name":"Florian Alexander","orcid":"0000-0001-7302-8256"}],"quality_controlled":"1","file":[{"file_id":"20281","content_type":"application/pdf","creator":"dernst","file_size":2484757,"success":1,"checksum":"89352f1f7e8d2b367ae5f4e9bf9eb1f5","relation":"main_file","date_created":"2025-09-03T06:44:44Z","access_level":"open_access","date_updated":"2025-09-03T06:44:44Z","file_name":"2025_SelectaMathematica_Browning.pdf"}],"article_type":"original","date_updated":"2025-09-30T14:29:25Z","OA_place":"publisher","_id":"20249","year":"2025","file_date_updated":"2025-09-03T06:44:44Z","scopus_import":"1","publication":"Selecta Mathematica New Series","month":"09","abstract":[{"text":"We develop a heuristic for the density of integer points on affine cubic surfaces. Our heuristic applies to smooth surfaces defined by cubic polynomials that are log K3, but it can also be adjusted to handle singular cubic surfaces. We compare our heuristic to Heath-Brown’s prediction for sums of three cubes, as well as to asymptotic formulae in the literature around Zagier’s work on the Markoff cubic surface, and work of Baragar and Umeda on further surfaces of Markoff-type. We also test our heuristic against numerical data for several families of cubic surfaces.","lang":"eng"}],"department":[{"_id":"TiBr"}]},{"has_accepted_license":"1","date_created":"2025-09-21T22:01:31Z","volume":393,"type":"journal_article","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","ec_funded":1,"acknowledgement":"The authors are very grateful to Alina Ostafe, Matthew Satriano and Igor Shparlinski for drawing their attention to this problem and for useful comments, and to Michael Larsen and Peter Sarnak for their helpful correspondence. We also thank the referee for their valuable input. While working on this paper the first author was supported by a FWF grant (DOI 10.55776/P36278), the second author by a Sloan Research Fellowship, and the third author by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Open access funding provided by Institute of Science and Technology (IST Austria).","ddc":["510"],"project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"intvolume":"       393","isi":1,"external_id":{"arxiv":["2409.01920"],"isi":["001567740200001"]},"oa":1,"OA_type":"hybrid","page":"1863–1880","language":[{"iso":"eng"}],"publication_status":"published","arxiv":1,"citation":{"ama":"Browning TD, Sawin W, Wang V. Pairs of commuting integer matrices. <i>Mathematische Annalen</i>. 2025;393:1863–1880. doi:<a href=\"https://doi.org/10.1007/s00208-025-03285-5\">10.1007/s00208-025-03285-5</a>","short":"T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen 393 (2025) 1863–1880.","ieee":"T. D. Browning, W. Sawin, and V. Wang, “Pairs of commuting integer matrices,” <i>Mathematische Annalen</i>, vol. 393. Springer Nature, pp. 1863–1880, 2025.","apa":"Browning, T. D., Sawin, W., &#38; Wang, V. (2025). Pairs of commuting integer matrices. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-025-03285-5\">https://doi.org/10.1007/s00208-025-03285-5</a>","mla":"Browning, Timothy D., et al. “Pairs of Commuting Integer Matrices.” <i>Mathematische Annalen</i>, vol. 393, Springer Nature, 2025, pp. 1863–1880, doi:<a href=\"https://doi.org/10.1007/s00208-025-03285-5\">10.1007/s00208-025-03285-5</a>.","chicago":"Browning, Timothy D, Will Sawin, and Victor Wang. “Pairs of Commuting Integer Matrices.” <i>Mathematische Annalen</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00208-025-03285-5\">https://doi.org/10.1007/s00208-025-03285-5</a>.","ista":"Browning TD, Sawin W, Wang V. 2025. Pairs of commuting integer matrices. Mathematische Annalen. 393, 1863–1880."},"_id":"20367","OA_place":"publisher","year":"2025","scopus_import":"1","file_date_updated":"2026-01-05T13:15:44Z","month":"10","publication":"Mathematische Annalen","abstract":[{"text":"We prove upper and lower bounds on the number of pairs of commuting n x n matrices with integer entries in [-T, T], as T -> . Our work uses Fourier analysis and leads to an analysis of exponential sums involving matrices over finite fields. These are bounded by combining a stratification result of Fouvry and Katz with a new result about the flatness of the commutator Lie bracket.","lang":"eng"}],"department":[{"_id":"TiBr"}],"corr_author":"1","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Will","full_name":"Sawin, Will","last_name":"Sawin"},{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","last_name":"Wang","full_name":"Wang, Victor","first_name":"Victor","orcid":"0000-0002-0704-7026"}],"quality_controlled":"1","article_type":"original","file":[{"date_updated":"2026-01-05T13:15:44Z","access_level":"open_access","file_name":"2025_MathAnnalen_Browning.pdf","file_size":337505,"file_id":"20950","creator":"dernst","content_type":"application/pdf","date_created":"2026-01-05T13:15:44Z","relation":"main_file","checksum":"1e94da1a67306e03c8e0086518faf4bc","success":1}],"date_updated":"2026-01-05T13:15:53Z","date_published":"2025-10-01T00:00:00Z","doi":"10.1007/s00208-025-03285-5","oa_version":"Published Version","PlanS_conform":"1","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"title":"Pairs of commuting integer matrices"},{"publication_identifier":{"eissn":["2363-9555"]},"title":"On the existence of magic squares of powers","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"issue":"4","PlanS_conform":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"23","doi":"10.1007/s40993-025-00671-5","date_published":"2025-09-23T00:00:00Z","oa_version":"Published Version","quality_controlled":"1","file":[{"date_updated":"2025-10-13T11:28:49Z","access_level":"open_access","file_name":"2025_ResearchNumberTheory_Rome.pdf","content_type":"application/pdf","file_id":"20463","creator":"dernst","file_size":428531,"checksum":"d41fbdc0cfc1fbceb519eb49b20a3ec2","relation":"main_file","date_created":"2025-10-13T11:28:49Z","success":1}],"article_type":"original","author":[{"last_name":"Rome","full_name":"Rome, Nick","first_name":"Nick"},{"id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","first_name":"Shuntaro","full_name":"Yamagishi, Shuntaro","last_name":"Yamagishi"}],"date_updated":"2025-10-13T12:30:40Z","corr_author":"1","abstract":[{"lang":"eng","text":"For any d  2, we prove that there exists an integer n0(d) such that there exists an n × n\r\nmagic square of dth powers for all n  n0(d). In particular, we establish the existence of\r\nan n × n magic square of squares for all n  4, which settles a conjecture of\r\nVárilly-Alvarado. All previous approaches had been based on constructive methods and\r\nthe existence of n × n magic squares of dth powers had only been known for sparse\r\nvalues of n. We prove our result by the Hardy-Littlewood circle method, which in this\r\nsetting essentially reduces the problem to finding a sufficient number of disjoint linearly\r\nindependent subsets of the columns of the coefficient matrix of the equations defining\r\nmagic squares. We prove an optimal (up to a constant) lower bound for this quantity."}],"month":"09","publication":"Research in Number Theory","department":[{"_id":"TiBr"}],"_id":"20423","OA_place":"publisher","file_date_updated":"2025-10-13T11:28:49Z","scopus_import":"1","year":"2025","arxiv":1,"citation":{"mla":"Rome, Nick, and Shuntaro Yamagishi. “On the Existence of Magic Squares of Powers.” <i>Research in Number Theory</i>, vol. 11, no. 4, 91, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s40993-025-00671-5\">10.1007/s40993-025-00671-5</a>.","apa":"Rome, N., &#38; Yamagishi, S. (2025). On the existence of magic squares of powers. <i>Research in Number Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s40993-025-00671-5\">https://doi.org/10.1007/s40993-025-00671-5</a>","chicago":"Rome, Nick, and Shuntaro Yamagishi. “On the Existence of Magic Squares of Powers.” <i>Research in Number Theory</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s40993-025-00671-5\">https://doi.org/10.1007/s40993-025-00671-5</a>.","ista":"Rome N, Yamagishi S. 2025. On the existence of magic squares of powers. Research in Number Theory. 11(4), 91.","ama":"Rome N, Yamagishi S. On the existence of magic squares of powers. <i>Research in Number Theory</i>. 2025;11(4). doi:<a href=\"https://doi.org/10.1007/s40993-025-00671-5\">10.1007/s40993-025-00671-5</a>","short":"N. Rome, S. Yamagishi, Research in Number Theory 11 (2025).","ieee":"N. Rome and S. Yamagishi, “On the existence of magic squares of powers,” <i>Research in Number Theory</i>, vol. 11, no. 4. Springer Nature, 2025."},"publication_status":"published","language":[{"iso":"eng"}],"OA_type":"hybrid","article_number":"91","external_id":{"arxiv":["2406.09364"]},"oa":1,"intvolume":"        11","ddc":["510"],"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","call_identifier":"FWF","grant_number":"P32428"}],"acknowledgement":"The authors are grateful to Tim Browning for his constant encouragement and enthusiasm, Jörg Brüdern for very helpful discussion regarding his paper [1] and Diyuan Wu for turning the proof of Theorem 2.4 in the original version into an algorithm and running the computation for us, for which the results are available in the appendix of the original version. They would also like to thank Christian Boyer for maintaining his website [4] which contains a comprehensive list of various magic squares discovered, Brady Haran and Tony Várilly-Alvarado for their public engagement activity of mathematics and magic squares of squares (A YouTube video “Magic Squares of Squares (are PROBABLY impossible)” of the Numberphile channel by Brady Haran, in which Tony Várilly-Alvarado appears as a guest speaker: https://www.youtube.com/watch?v=Kdsj84UdeYg.), and all the magic squares enthusiasts who have contributed to [4] which made this paper possible. Finally, the authors would like to thank the anonymous referees for their helpful comments, Daniel Flores for his work [11] which inspired them to optimise the proof of Theorem 2.4 and Trevor Wooley for very helpful discussion regarding recent developments in Waring’s problem and his comments on the original version of this paper.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). NR was supported by FWF project ESP 441-NBL while SY by a FWF grant (DOI 10.55776/P32428).","type":"journal_article","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","volume":11,"has_accepted_license":"1","date_created":"2025-10-05T22:01:34Z"},{"title":"Sumset growth in progression-free sets","publication_identifier":{"issn":["0065-1036"],"eissn":["1730-6264"]},"oa_version":"None","doi":"10.4064/aa250115-14-7","date_published":"2025-09-12T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"12","corr_author":"1","date_updated":"2025-12-01T15:18:09Z","article_type":"original","quality_controlled":"1","author":[{"full_name":"Elsholtz, Christian","first_name":"Christian","last_name":"Elsholtz"},{"last_name":"Ruzsa","full_name":"Ruzsa, Imre Z.","first_name":"Imre Z."},{"full_name":"Wurzinger, Lena","first_name":"Lena","last_name":"Wurzinger","orcid":"0009-0004-5360-0074","id":"50c57d72-32a8-11ee-aeea-d652094d2ccd"}],"scopus_import":"1","year":"2025","_id":"20603","department":[{"_id":"TiBr"}],"abstract":[{"lang":"eng","text":"We study the growth of sumsets A+B⊂S⊂G, where S does not contain an arithmetic progression of length 2k+1, and where G is a commutative group, in which every nonzero element has an order of at least 2k+1. More specifically, we show the following: if A,B⊂G are sets such that A+B does not contain an arithmetic progression of length 2k+1, then\r\n|A+B|≥|A|2k−13k−2|B|k3k−2.\r\nAs an application we derive upper bounds on the cardinality of the summands in sumsets A+B+C contained in the set of t-th powers, where t≥2 is an integer. In particular, we show that min(|A|,|B|,|C|)≪(logN)4/5 for t=2, and min(|A|,|B|,|C|)≪t(logN)1/2 for t≥3."}],"month":"09","publication":"Acta Arithmetica","language":[{"iso":"eng"}],"publication_status":"published","citation":{"chicago":"Elsholtz, Christian, Imre Z. Ruzsa, and Lena Wurzinger. “Sumset Growth in Progression-Free Sets.” <i>Acta Arithmetica</i>. Institute of Mathematics, 2025. <a href=\"https://doi.org/10.4064/aa250115-14-7\">https://doi.org/10.4064/aa250115-14-7</a>.","mla":"Elsholtz, Christian, et al. “Sumset Growth in Progression-Free Sets.” <i>Acta Arithmetica</i>, vol. 220, Institute of Mathematics, 2025, pp. 289–303, doi:<a href=\"https://doi.org/10.4064/aa250115-14-7\">10.4064/aa250115-14-7</a>.","apa":"Elsholtz, C., Ruzsa, I. Z., &#38; Wurzinger, L. (2025). Sumset growth in progression-free sets. <i>Acta Arithmetica</i>. Institute of Mathematics. <a href=\"https://doi.org/10.4064/aa250115-14-7\">https://doi.org/10.4064/aa250115-14-7</a>","ista":"Elsholtz C, Ruzsa IZ, Wurzinger L. 2025. Sumset growth in progression-free sets. Acta Arithmetica. 220, 289–303.","ieee":"C. Elsholtz, I. Z. Ruzsa, and L. Wurzinger, “Sumset growth in progression-free sets,” <i>Acta Arithmetica</i>, vol. 220. Institute of Mathematics, pp. 289–303, 2025.","ama":"Elsholtz C, Ruzsa IZ, Wurzinger L. Sumset growth in progression-free sets. <i>Acta Arithmetica</i>. 2025;220:289-303. doi:<a href=\"https://doi.org/10.4064/aa250115-14-7\">10.4064/aa250115-14-7</a>","short":"C. Elsholtz, I.Z. Ruzsa, L. Wurzinger, Acta Arithmetica 220 (2025) 289–303."},"external_id":{"isi":["001570716800001"]},"isi":1,"page":"289-303","OA_type":"closed access","intvolume":"       220","date_created":"2025-11-04T14:33:16Z","acknowledgement":"The authors would like to thank the referee and Ilya Shkredov for comments on the manuscript.\r\nC. E. is supported by a joint FWF-ANR project ArithRand, grant numbers FWF I 4945-N and ANR-20-CE91-0006.\r\n","article_processing_charge":"No","type":"journal_article","volume":220,"publisher":"Institute of Mathematics"},{"citation":{"ieee":"V. Wang, “Diagonal cubic forms and the large sieve,” <i>Mathematika</i>, vol. 71, no. 1. London Mathematical Society, 2025.","short":"V. Wang, Mathematika 71 (2025).","ama":"Wang V. Diagonal cubic forms and the large sieve. <i>Mathematika</i>. 2025;71(1). doi:<a href=\"https://doi.org/10.1112/mtk.70008\">10.1112/mtk.70008</a>","ista":"Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1), e70008.","mla":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” <i>Mathematika</i>, vol. 71, no. 1, e70008, London Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.1112/mtk.70008\">10.1112/mtk.70008</a>.","apa":"Wang, V. (2025). Diagonal cubic forms and the large sieve. <i>Mathematika</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/mtk.70008\">https://doi.org/10.1112/mtk.70008</a>","chicago":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” <i>Mathematika</i>. London Mathematical Society, 2025. <a href=\"https://doi.org/10.1112/mtk.70008\">https://doi.org/10.1112/mtk.70008</a>."},"publication_status":"published","language":[{"iso":"eng"}],"OA_type":"hybrid","isi":1,"external_id":{"isi":["001388255500001"]},"oa":1,"article_number":"e70008","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"ddc":["510"],"intvolume":"        71","type":"journal_article","volume":71,"publisher":"London Mathematical Society","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"acknowledgement":"I thank Peter Sarnak for suggesting projects that ultimately led to the present paper. I also thank him for many encouraging discussions, helpful comments, and references. Thanks also to Tim Browning, Trevor Wooley, and Nina Zubrilina for helpful comments, and to Levent Alpöge and Will Sawin for some interesting old discussions. I thank Yang Liu, Evan O'Dorney, Ashwin Sah, and Mark Sellke for conversations illuminating the combinatorics of an older, counting version of the present Lemma 4.9. Finally, special thanks are due to the editors and referees for their patience and help with the exposition. This work was partially supported by NSF Grant DMS-1802211, and the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","date_created":"2025-01-12T23:04:01Z","has_accepted_license":"1","publication_identifier":{"eissn":["2041-7942"],"issn":["0025-5793"]},"title":"Diagonal cubic forms and the large sieve","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"issue":"1","day":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2025-01-02T00:00:00Z","doi":"10.1112/mtk.70008","oa_version":"Published Version","author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","orcid":"0000-0002-0704-7026","last_name":"Wang","first_name":"Victor","full_name":"Wang, Victor"}],"quality_controlled":"1","article_type":"original","file":[{"creator":"dernst","content_type":"application/pdf","file_id":"18845","file_size":309893,"checksum":"700a8596b4bffce2320d074120962c22","date_created":"2025-01-14T06:52:09Z","relation":"main_file","success":1,"date_updated":"2025-01-14T06:52:09Z","access_level":"open_access","file_name":"2025_Mathematika_Wang.pdf"}],"date_updated":"2025-04-14T07:54:56Z","corr_author":"1","month":"01","publication":"Mathematika","abstract":[{"text":"Let N(X) be the number of integral zeros (mathematical equation). Works of Hooley and Heath-Brown imply (mathematical equation), if one assumes automorphy and grand Riemann hypothesis for certain Hasse–Weil L-functions. Assuming instead a natural large sieve inequality, we recover the same bound on N(X). This is part of a more general statement, for diagonal cubic forms in (mathematical equation) variables, where we allow approximations to Hasse–Weil L-functions.","lang":"eng"}],"department":[{"_id":"TiBr"}],"OA_place":"publisher","_id":"18822","year":"2025","file_date_updated":"2025-01-14T06:52:09Z","scopus_import":"1"},{"project":[{"grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"ddc":["510"],"intvolume":"        19","date_created":"2025-02-18T13:33:14Z","has_accepted_license":"1","publisher":"Mathematical Sciences Publishers","type":"journal_article","article_processing_charge":"No","volume":19,"ec_funded":1,"acknowledgement":"I am very grateful to my Ph.D. advisor Emmanuel Peyre for all the remarks and suggestions he made during the writing of this article. I warmly thank Margaret Bilu and Tim Browning for some valuable comments they made on a preliminary version of this work. I would like to thank David Bourqui as well for several helpful conversations. Finally, I thank the anonymous referee for their very careful reading and their numerous comments and suggestions which helped me a lot in improving the exposition, besides fixing several typos, and Elizabeth Weaver for the final editing work. During the revision process of this work, the author received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","publication_status":"published","language":[{"iso":"eng"}],"arxiv":1,"citation":{"short":"L. Faisant, Algebra &#38; Number Theory 19 (2025) 883–965.","ama":"Faisant L. Motivic distribution of rational curves and twisted products of toric varieties. <i>Algebra &#38; Number Theory</i>. 2025;19:883-965. doi:<a href=\"https://doi.org/10.2140/ant.2025.19.883\">10.2140/ant.2025.19.883</a>","ieee":"L. Faisant, “Motivic distribution of rational curves and twisted products of toric varieties,” <i>Algebra &#38; Number Theory</i>, vol. 19. Mathematical Sciences Publishers, pp. 883–965, 2025.","ista":"Faisant L. 2025. Motivic distribution of rational curves and twisted products of toric varieties. Algebra &#38; Number Theory. 19, 883–965.","apa":"Faisant, L. (2025). Motivic distribution of rational curves and twisted products of toric varieties. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2025.19.883\">https://doi.org/10.2140/ant.2025.19.883</a>","chicago":"Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/ant.2025.19.883\">https://doi.org/10.2140/ant.2025.19.883</a>.","mla":"Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” <i>Algebra &#38; Number Theory</i>, vol. 19, Mathematical Sciences Publishers, 2025, pp. 883–965, doi:<a href=\"https://doi.org/10.2140/ant.2025.19.883\">10.2140/ant.2025.19.883</a>."},"external_id":{"arxiv":["2302.07339"]},"oa":1,"OA_type":"diamond","page":"883-965","corr_author":"1","author":[{"id":"26ca6926-5797-11ee-9232-f8b51bd19631","last_name":"Faisant","first_name":"Loïs","full_name":"Faisant, Loïs"}],"article_type":"original","quality_controlled":"1","file":[{"content_type":"application/pdf","file_id":"21307","creator":"dernst","file_size":2034433,"success":1,"checksum":"56299f55682528a7cd0136497ce8b383","date_created":"2026-02-17T13:17:00Z","relation":"main_file","access_level":"open_access","date_updated":"2026-02-17T13:17:00Z","file_name":"2025_AlgebraNumberTheory_Faisant.pdf"}],"date_updated":"2026-02-17T13:19:19Z","OA_place":"publisher","_id":"19054","year":"2025","file_date_updated":"2026-02-17T13:17:00Z","publication":"Algebra & Number Theory","month":"04","abstract":[{"lang":"eng","text":"This work concerns asymptotical stabilisation phenomena occurring in the moduli space of sections of certain algebraic families over a smooth projective curve, whenever the generic fibre of the family is a smooth projective Fano variety, or not far from being Fano.\r\n We describe the expected behaviour of the class, in a ring of motivic integration, of the moduli space of sections of given numerical class. Up to an adequate normalisation, it should converge, when the class of the sections goes arbitrarily far from the boundary of the dual of the effective cone, to an effective element given by a motivic Euler product. Such a principle can be seen as an analogue for rational curves of the Batyrev-Manin-Peyre principle for rational points.\r\n The central tool of this article is the property of equidistribution of curves. We show that this notion does not depend on the choice of a model of the generic fibre, and that equidistribution of curves holds for smooth projective split toric varieties. As an application, we study the Batyrev-Manin-Peyre principle for curves on a certain kind of twisted products."}],"department":[{"_id":"TiBr"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"eissn":["1944-7833"]},"title":"Motivic distribution of rational curves and twisted products of toric varieties","date_published":"2025-04-22T00:00:00Z","doi":"10.2140/ant.2025.19.883","oa_version":"Published Version","PlanS_conform":"1","day":"22","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public"},{"arxiv":1,"citation":{"chicago":"Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">https://doi.org/10.48550/ARXIV.2502.11704</a>.","mla":"Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” <i>ArXiv</i>, 2502.11704, doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">10.48550/ARXIV.2502.11704</a>.","apa":"Faisant, L. (n.d.). Motivic counting of rational curves with tangency conditions via universal torsors. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">https://doi.org/10.48550/ARXIV.2502.11704</a>","ista":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704.","ama":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">10.48550/ARXIV.2502.11704</a>","short":"L. Faisant, ArXiv (n.d.).","ieee":"L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” <i>arXiv</i>. ."},"language":[{"iso":"eng"}],"publication_status":"submitted","OA_type":"green","article_number":"2502.11704","external_id":{"arxiv":["2502.11704"]},"oa":1,"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"acknowledgement":"The author acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.\r\n","type":"preprint","article_processing_charge":"No","ec_funded":1,"date_created":"2025-02-18T13:34:07Z","title":"Motivic counting of rational curves with tangency conditions via universal torsors","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","day":"17","doi":"10.48550/ARXIV.2502.11704","date_published":"2025-02-17T00:00:00Z","oa_version":"Preprint","author":[{"id":"26ca6926-5797-11ee-9232-f8b51bd19631","last_name":"Faisant","first_name":"Loïs","full_name":"Faisant, Loïs"}],"date_updated":"2025-04-14T07:54:52Z","corr_author":"1","abstract":[{"text":"Using the formalism of Cox rings and universal torsors, we prove a decomposition of the Grothendieck motive of the moduli space of morphisms from an arbitrary smooth projective curve to a Mori Dream Space (MDS).\r\n For the simplest cases of MDS, that of toric varieties, we use this decomposition to prove an instance of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency conditions with respect to the boundary divisors, often called Campana curves.","lang":"eng"}],"publication":"arXiv","month":"02","department":[{"_id":"TiBr"}],"OA_place":"repository","_id":"19055","year":"2025","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.11704","open_access":"1"}]},{"intvolume":"       273","ddc":["510"],"date_created":"2025-03-09T23:01:26Z","has_accepted_license":"1","publisher":"Elsevier","article_processing_charge":"Yes (in subscription journal)","volume":273,"type":"journal_article","publication_status":"published","language":[{"iso":"eng"}],"citation":{"ama":"Chan S, Koymans P, Pagano C, Sofos E. Averages of multiplicative functions along equidistributed sequences. <i>Journal of Number Theory</i>. 2025;273:1-36. doi:<a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">10.1016/j.jnt.2025.01.005</a>","short":"S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025) 1–36.","ieee":"S. Chan, P. Koymans, C. Pagano, and E. Sofos, “Averages of multiplicative functions along equidistributed sequences,” <i>Journal of Number Theory</i>, vol. 273. Elsevier, pp. 1–36, 2025.","chicago":"Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “Averages of Multiplicative Functions along Equidistributed Sequences.” <i>Journal of Number Theory</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">https://doi.org/10.1016/j.jnt.2025.01.005</a>.","apa":"Chan, S., Koymans, P., Pagano, C., &#38; Sofos, E. (2025). Averages of multiplicative functions along equidistributed sequences. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">https://doi.org/10.1016/j.jnt.2025.01.005</a>","mla":"Chan, Stephanie, et al. “Averages of Multiplicative Functions along Equidistributed Sequences.” <i>Journal of Number Theory</i>, vol. 273, Elsevier, 2025, pp. 1–36, doi:<a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">10.1016/j.jnt.2025.01.005</a>.","ista":"Chan S, Koymans P, Pagano C, Sofos E. 2025. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 273, 1–36."},"isi":1,"oa":1,"external_id":{"isi":["001444208500001"]},"page":"1-36","OA_type":"hybrid","corr_author":"1","file":[{"access_level":"open_access","date_updated":"2025-12-30T08:05:42Z","file_name":"2025_JourNumberTheory_Chan.pdf","file_size":685204,"file_id":"20889","creator":"dernst","content_type":"application/pdf","success":1,"relation":"main_file","date_created":"2025-12-30T08:05:42Z","checksum":"752c407eb186d391380b10a7505f66cf"}],"article_type":"original","quality_controlled":"1","author":[{"id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","full_name":"Chan, Yik Tung","first_name":"Yik Tung","last_name":"Chan","orcid":"0000-0001-8467-4106"},{"last_name":"Koymans","full_name":"Koymans, Peter","first_name":"Peter"},{"last_name":"Pagano","full_name":"Pagano, Carlo","first_name":"Carlo"},{"first_name":"Efthymios","full_name":"Sofos, Efthymios","last_name":"Sofos"}],"date_updated":"2025-12-30T08:06:16Z","_id":"19363","OA_place":"publisher","file_date_updated":"2025-12-30T08:05:42Z","scopus_import":"1","year":"2025","abstract":[{"text":"For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.","lang":"eng"}],"month":"08","publication":"Journal of Number Theory","department":[{"_id":"TiBr"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"issn":["0022-314X"]},"title":"Averages of multiplicative functions along equidistributed sequences","doi":"10.1016/j.jnt.2025.01.005","date_published":"2025-08-01T00:00:00Z","oa_version":"Published Version","PlanS_conform":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01"},{"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"07","oa_version":"Preprint","doi":"10.2422/2036-2145.202412_006","date_published":"2025-03-07T00:00:00Z","title":"6-torision and integral points on quartic threefolds","publication_identifier":{"issn":["0391-173X"],"eissn":["2036-2145"]},"department":[{"_id":"TiBr"}],"abstract":[{"lang":"eng","text":"We prove matching upper and lower bounds for the average of the6-torsionof class groups of quadratic fields. Furthermore, we count the number of integer solutions on an affine quartic threefold."}],"month":"03","publication":"Annali della Scuola Normale Superiore di Pisa, Classe di Scienze","year":"2025","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2403.13359"}],"_id":"19483","OA_place":"repository","date_updated":"2025-05-14T11:40:24Z","article_type":"original","author":[{"orcid":"0000-0001-8467-4106","last_name":"Chan","full_name":"Chan, Yik Tung","first_name":"Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1"},{"last_name":"Koymans","first_name":"Peter","full_name":"Koymans, Peter"},{"last_name":"Pagano","first_name":"Carlo","full_name":"Pagano, Carlo"},{"full_name":"Sofos, Efthymios","first_name":"Efthymios","last_name":"Sofos"}],"corr_author":"1","OA_type":"green","article_number":"18","external_id":{"arxiv":["2403.13359"]},"oa":1,"citation":{"ieee":"S. Chan, P. Koymans, C. Pagano, and E. Sofos, “6-torision and integral points on quartic threefolds,” <i>Annali della Scuola Normale Superiore di Pisa, Classe di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale, 2025.","short":"S. Chan, P. Koymans, C. Pagano, E. Sofos, Annali Della Scuola Normale Superiore Di Pisa, Classe Di Scienze (2025).","ama":"Chan S, Koymans P, Pagano C, Sofos E. 6-torision and integral points on quartic threefolds. <i>Annali della Scuola Normale Superiore di Pisa, Classe di Scienze</i>. 2025. doi:<a href=\"https://doi.org/10.2422/2036-2145.202412_006\">10.2422/2036-2145.202412_006</a>","ista":"Chan S, Koymans P, Pagano C, Sofos E. 2025. 6-torision and integral points on quartic threefolds. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze., 18.","apa":"Chan, S., Koymans, P., Pagano, C., &#38; Sofos, E. (2025). 6-torision and integral points on quartic threefolds. <i>Annali Della Scuola Normale Superiore Di Pisa, Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale. <a href=\"https://doi.org/10.2422/2036-2145.202412_006\">https://doi.org/10.2422/2036-2145.202412_006</a>","mla":"Chan, Stephanie, et al. “6-Torision and Integral Points on Quartic Threefolds.” <i>Annali Della Scuola Normale Superiore Di Pisa, Classe Di Scienze</i>, 18, Scuola Normale Superiore - Edizioni della Normale, 2025, doi:<a href=\"https://doi.org/10.2422/2036-2145.202412_006\">10.2422/2036-2145.202412_006</a>.","chicago":"Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “6-Torision and Integral Points on Quartic Threefolds.” <i>Annali Della Scuola Normale Superiore Di Pisa, Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale, 2025. <a href=\"https://doi.org/10.2422/2036-2145.202412_006\">https://doi.org/10.2422/2036-2145.202412_006</a>."},"arxiv":1,"language":[{"iso":"eng"}],"publication_status":"epub_ahead","article_processing_charge":"No","publisher":"Scuola Normale Superiore - Edizioni della Normale","type":"journal_article","date_created":"2025-04-05T10:49:27Z"},{"ddc":["510"],"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"intvolume":"         3","date_created":"2025-05-11T22:02:41Z","has_accepted_license":"1","ec_funded":1,"type":"journal_article","article_processing_charge":"No","publisher":"Association for Mathematical Research","volume":3,"acknowledgement":"This work was partially supported by the European Union’s Horizon 2020 research and innovation program under the MarieSkłodowska-Curie Grant Agreement No. 101034413","publication_status":"published","language":[{"iso":"eng"}],"citation":{"ista":"Wang V. 2025. Prime Hasse principles via diophantine second moments. Journal of the Association for Mathematical Research. 3(1), 1–26.","mla":"Wang, Victor. “Prime Hasse Principles via Diophantine Second Moments.” <i>Journal of the Association for Mathematical Research</i>, vol. 3, no. 1, Association for Mathematical Research, 2025, pp. 1–26, doi:<a href=\"https://doi.org/10.56994/JAMR.003.001.001\">10.56994/JAMR.003.001.001</a>.","chicago":"Wang, Victor. “Prime Hasse Principles via Diophantine Second Moments.” <i>Journal of the Association for Mathematical Research</i>. Association for Mathematical Research, 2025. <a href=\"https://doi.org/10.56994/JAMR.003.001.001\">https://doi.org/10.56994/JAMR.003.001.001</a>.","apa":"Wang, V. (2025). Prime Hasse principles via diophantine second moments. <i>Journal of the Association for Mathematical Research</i>. Association for Mathematical Research. <a href=\"https://doi.org/10.56994/JAMR.003.001.001\">https://doi.org/10.56994/JAMR.003.001.001</a>","short":"V. Wang, Journal of the Association for Mathematical Research 3 (2025) 1–26.","ama":"Wang V. Prime Hasse principles via diophantine second moments. <i>Journal of the Association for Mathematical Research</i>. 2025;3(1):1-26. doi:<a href=\"https://doi.org/10.56994/JAMR.003.001.001\">10.56994/JAMR.003.001.001</a>","ieee":"V. Wang, “Prime Hasse principles via diophantine second moments,” <i>Journal of the Association for Mathematical Research</i>, vol. 3, no. 1. Association for Mathematical Research, pp. 1–26, 2025."},"arxiv":1,"external_id":{"arxiv":["2304.08674"]},"oa":1,"OA_type":"diamond","page":"1-26","corr_author":"1","date_updated":"2025-05-12T10:26:00Z","author":[{"full_name":"Wang, Victor","first_name":"Victor","last_name":"Wang","orcid":"0000-0002-0704-7026","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9"}],"file":[{"access_level":"open_access","date_updated":"2025-05-12T10:23:26Z","file_name":"2025_JAMR_Wang.pdf","file_size":1094167,"file_id":"19682","content_type":"application/pdf","creator":"dernst","success":1,"date_created":"2025-05-12T10:23:26Z","relation":"main_file","checksum":"f9a1057d146632890466a7dc33bf625e"}],"quality_controlled":"1","article_type":"original","year":"2025","file_date_updated":"2025-05-12T10:23:26Z","scopus_import":"1","_id":"19673","OA_place":"publisher","department":[{"_id":"TiBr"}],"publication":"Journal of the Association for Mathematical Research","month":"01","abstract":[{"lang":"eng","text":"We show that almost all primes p =\\= ± 4 mod9 are sums of three cubes, assuming a conjecture due to Hooley, Manin, et al. on cubic fourfolds. This conjecture is approachable under standard statistical hypotheses on geometric families of L-functions."}],"tmp":{"short":"CC BY-NC (4.0)","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"title":"Prime Hasse principles via diophantine second moments","publication_identifier":{"eissn":["2998-4114"]},"oa_version":"Published Version","date_published":"2025-01-23T00:00:00Z","doi":"10.56994/JAMR.003.001.001","day":"23","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1"},{"title":"Asymptotic growth of translation-dilation orbits","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","PlanS_conform":"1","oa_version":"Published Version","doi":"10.1016/j.aim.2025.110341","date_published":"2025-07-01T00:00:00Z","date_updated":"2025-12-30T08:30:30Z","quality_controlled":"1","article_type":"original","file":[{"file_name":"2025_AdvMathematics_Wang.pdf","date_updated":"2025-12-30T08:30:17Z","access_level":"open_access","relation":"main_file","date_created":"2025-12-30T08:30:17Z","checksum":"01f2589b678ba840d6a4066c1d8d7642","success":1,"file_size":1592341,"file_id":"20895","content_type":"application/pdf","creator":"dernst"}],"author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","full_name":"Wang, Victor","first_name":"Victor","last_name":"Wang","orcid":"0000-0002-0704-7026"}],"corr_author":"1","department":[{"_id":"TiBr"}],"abstract":[{"lang":"eng","text":"By studying some Clausen-like multiple Dirichlet series, we complete the proof of Manin's conjecture for sufficiently split smooth equivariant compactifications of the translation-dilation group over the rationals. Secondary terms remain elusive in general."}],"publication":"Advances in Mathematics","month":"07","file_date_updated":"2025-12-30T08:30:17Z","scopus_import":"1","year":"2025","_id":"19727","OA_place":"publisher","citation":{"ieee":"V. Wang, “Asymptotic growth of translation-dilation orbits,” <i>Advances in Mathematics</i>, vol. 475. Elsevier, 2025.","ama":"Wang V. Asymptotic growth of translation-dilation orbits. <i>Advances in Mathematics</i>. 2025;475. doi:<a href=\"https://doi.org/10.1016/j.aim.2025.110341\">10.1016/j.aim.2025.110341</a>","short":"V. Wang, Advances in Mathematics 475 (2025).","apa":"Wang, V. (2025). Asymptotic growth of translation-dilation orbits. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2025.110341\">https://doi.org/10.1016/j.aim.2025.110341</a>","chicago":"Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” <i>Advances in Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.aim.2025.110341\">https://doi.org/10.1016/j.aim.2025.110341</a>.","mla":"Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” <i>Advances in Mathematics</i>, vol. 475, 110341, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.aim.2025.110341\">10.1016/j.aim.2025.110341</a>.","ista":"Wang V. 2025. Asymptotic growth of translation-dilation orbits. Advances in Mathematics. 475, 110341."},"arxiv":1,"publication_status":"published","language":[{"iso":"eng"}],"OA_type":"hybrid","article_number":"110341","oa":1,"external_id":{"isi":["001495142300002"],"arxiv":["2309.07626"]},"isi":1,"intvolume":"       475","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"ddc":["510"],"acknowledgement":"I thank Yuri Tschinkel for introducing me to the beautiful paper [53] and associated open questions, and thank him as well as Ramin Takloo-Bighash and Sho Tanimoto for their encouragement and comments. Also, I thank Tim Browning and Dan Loughran for comments and suggestions concerning Manin–Peyre, homogeneous spaces, and splitness. Thanks also to Anshul Adve, Peter Sarnak, Philip Tosteson, Katy Woo, and Nina Zubrilina for some interesting discussions. I thank the Browning Group and Andy O'Desky for many conversations. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Finally, I thank the editors and referees for their detailed input, which substantially improved the paper.","volume":475,"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","publisher":"Elsevier","type":"journal_article","has_accepted_license":"1","date_created":"2025-05-25T22:16:41Z"},{"has_accepted_license":"1","date_created":"2025-06-03T07:30:21Z","ec_funded":1,"type":"journal_article","publisher":"Springer Nature","volume":310,"article_processing_charge":"Yes (via OA deal)","acknowledgement":"We thank Alexandra Florea for discussions on cubic Gauss sums over function fields, in addition to the anonymous referee for helpful comments. While working on this paper the first two authors were supported by a FWF grant (DOI 10.55776/P36278) and the third author was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Open access funding provided by Institute of Science and Technology (IST Austria).","project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"ddc":["510"],"intvolume":"       310","oa":1,"external_id":{"isi":["001494367000001"],"arxiv":["2408.03668 "]},"article_number":"65","isi":1,"OA_type":"hybrid","language":[{"iso":"eng"}],"publication_status":"published","citation":{"ista":"Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 310(4), 65.","apa":"Browning, T. D., Glas, J., &#38; Wang, V. (2025). Optimal sums of three cubes in Fq[t]. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-025-03765-z\">https://doi.org/10.1007/s00209-025-03765-z</a>","mla":"Browning, Timothy D., et al. “Optimal Sums of Three Cubes in Fq[T].” <i>Mathematische Zeitschrift</i>, vol. 310, no. 4, 65, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00209-025-03765-z\">10.1007/s00209-025-03765-z</a>.","chicago":"Browning, Timothy D, Jakob Glas, and Victor Wang. “Optimal Sums of Three Cubes in Fq[T].” <i>Mathematische Zeitschrift</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00209-025-03765-z\">https://doi.org/10.1007/s00209-025-03765-z</a>.","ieee":"T. D. Browning, J. Glas, and V. Wang, “Optimal sums of three cubes in Fq[t],” <i>Mathematische Zeitschrift</i>, vol. 310, no. 4. Springer Nature, 2025.","short":"T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025).","ama":"Browning TD, Glas J, Wang V. Optimal sums of three cubes in Fq[t]. <i>Mathematische Zeitschrift</i>. 2025;310(4). doi:<a href=\"https://doi.org/10.1007/s00209-025-03765-z\">10.1007/s00209-025-03765-z</a>"},"arxiv":1,"year":"2025","file_date_updated":"2025-06-03T08:28:14Z","scopus_import":"1","_id":"19776","OA_place":"publisher","department":[{"_id":"TiBr"}],"publication":"Mathematische Zeitschrift","month":"05","abstract":[{"lang":"eng","text":"We use the circle method to prove that a density 1 of elements in Fq[t] are representable as a sum of three cubes of essentially minimal degree from Fq[t], assuming the Ratios Conjecture and that char(Fq)>3. Roughly speaking, to do so, we upgrade an order of magnitude result to a full asymptotic formula that was conjectured by Hooley in the number field setting."}],"corr_author":"1","date_updated":"2025-09-30T12:43:41Z","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jakob","full_name":"Glas, Jakob","last_name":"Glas","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb"},{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","last_name":"Wang","full_name":"Wang, Victor","first_name":"Victor","orcid":"0000-0002-0704-7026"}],"quality_controlled":"1","article_type":"original","file":[{"success":1,"date_created":"2025-06-03T08:28:14Z","relation":"main_file","checksum":"6f71e25740c28257bf89b8bf116c2b4d","file_size":461622,"content_type":"application/pdf","file_id":"19782","creator":"dernst","file_name":"2025_MathZeitschrift_Browning.pdf","access_level":"open_access","date_updated":"2025-06-03T08:28:14Z"}],"oa_version":"Published Version","date_published":"2025-05-23T00:00:00Z","doi":"10.1007/s00209-025-03765-z","day":"23","status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","issue":"4","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"title":"Optimal sums of three cubes in Fq[t]","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]}},{"year":"2025","scopus_import":"1","file_date_updated":"2025-12-29T10:05:22Z","OA_place":"publisher","_id":"20850","department":[{"_id":"TiBr"}],"publication":"Journal de theorie des nombres de Bordeaux","month":"11","abstract":[{"lang":"eng","text":"We provide an estimate for the number of nontrivial integer points on the Pellian surface t^2 - du^2 = 1 in a bounded region. We give a lower bound on the size of fundamental solutions for almost all d in a certain class, based on a recent conjecture of Browning and Wilsch about integer points on log K3 surfaces. We also obtain an upper bound on the average of class number in this class, assuming the same conjecture."},{"text":"Nous donnons une estimation du nombre de points entiers non triviaux sur la surface pellienne \r\nt^2 - du^2 = 1 dans une région bornée. Nous établissons une borne inférieure pour la taille des solutions fondamentales pour presque tout d appartenant à une certaine classe, en nous fondant sur une conjecture récente de Browning et Wilsch concernant les points entiers sur les surfaces log K3. Nous obtenons également une borne supérieure pour la moyenne du nombre de classes dans cette classe, sous la même hypothèse conjecturale.","lang":"fre"}],"corr_author":"1","date_updated":"2025-12-29T10:08:46Z","author":[{"orcid":"0000-0002-4989-5330","last_name":"Diao","full_name":"Diao, Yijie","first_name":"Yijie","id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b"}],"article_type":"original","file":[{"success":1,"checksum":"67aa0afbc0b5bcbff5341f4d25e6ba20","date_created":"2025-12-29T10:05:22Z","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_id":"20861","file_size":766196,"file_name":"2025_JTNB_Diao.pdf","access_level":"open_access","date_updated":"2025-12-29T10:05:22Z"}],"quality_controlled":"1","oa_version":"Published Version","date_published":"2025-11-27T00:00:00Z","doi":"10.5802/jtnb.1348","day":"27","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","issue":"3","tmp":{"image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode"},"title":"Class numbers and integer points on some Pellian surfaces","publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"date_created":"2025-12-21T23:01:35Z","has_accepted_license":"1","article_processing_charge":"Yes (in subscription journal)","volume":37,"publisher":"Université de Bordeaux","type":"journal_article","acknowledgement":"The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and useful comments. Moreover, he is grateful to Jakob Glas, Damaris Schindler, Igor Shparlinski, Matteo Verzobio, Victor Wang, Florian Wilsch and Shuntaro Yamagishi for taking their time to answer his questions and their valuable suggestions.","ddc":["510"],"intvolume":"        37","external_id":{"arxiv":["2408.03774"]},"oa":1,"OA_type":"hybrid","page":"973-988","language":[{"iso":"eng"}],"publication_status":"published","citation":{"ista":"Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 37(3), 973–988.","chicago":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux, 2025. <a href=\"https://doi.org/10.5802/jtnb.1348\">https://doi.org/10.5802/jtnb.1348</a>.","apa":"Diao, Y. (2025). Class numbers and integer points on some Pellian surfaces. <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux. <a href=\"https://doi.org/10.5802/jtnb.1348\">https://doi.org/10.5802/jtnb.1348</a>","mla":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” <i>Journal de Theorie Des Nombres de Bordeaux</i>, vol. 37, no. 3, Université de Bordeaux, 2025, pp. 973–88, doi:<a href=\"https://doi.org/10.5802/jtnb.1348\">10.5802/jtnb.1348</a>.","ieee":"Y. Diao, “Class numbers and integer points on some Pellian surfaces,” <i>Journal de theorie des nombres de Bordeaux</i>, vol. 37, no. 3. Université de Bordeaux, pp. 973–988, 2025.","short":"Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988.","ama":"Diao Y. Class numbers and integer points on some Pellian surfaces. <i>Journal de theorie des nombres de Bordeaux</i>. 2025;37(3):973-988. doi:<a href=\"https://doi.org/10.5802/jtnb.1348\">10.5802/jtnb.1348</a>"},"arxiv":1},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"title":"Counting integer points on affine surfaces with a side condition","publication_identifier":{"eissn":["2397-3129"]},"oa_version":"Published Version","date_published":"2025-09-01T00:00:00Z","doi":"10.19086/da.143787","day":"01","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","date_updated":"2026-02-12T08:03:12Z","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","full_name":"Browning, Timothy D","last_name":"Browning"},{"last_name":"Verzobio","full_name":"Verzobio, Matteo","first_name":"Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"article_type":"original","file":[{"creator":"dernst","file_id":"21214","content_type":"application/pdf","file_size":393625,"success":1,"checksum":"3d38e850b40f3e1abbfd30073bd4388a","date_created":"2026-02-12T07:50:47Z","relation":"main_file","access_level":"open_access","date_updated":"2026-02-12T07:50:47Z","file_name":"2025_DiscreteAnalysis_Browning.pdf"}],"year":"2025","file_date_updated":"2026-02-12T07:50:47Z","scopus_import":"1","OA_place":"publisher","_id":"21003","department":[{"_id":"TiBr"}],"month":"09","publication":"Discrete Analysis","abstract":[{"lang":"eng","text":"We extend work of Heath-Brown and Salberger, based on the determinant method, to provide a uniform upper bound for the number of integral points of bounded height on an affine surface, which are subject to a polynomial congruence condition. This is applied to get a new uniform bound for points on diagonal quadric surfaces, and to a problem about the representation of integers as a sum of four unlike powers."}],"language":[{"iso":"eng"}],"publication_status":"published","citation":{"mla":"Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” <i>Discrete Analysis</i>, vol. 2025, 12, Cambridge: Alliance of Diamond Open Access Journals, 2025, doi:<a href=\"https://doi.org/10.19086/da.143787\">10.19086/da.143787</a>.","apa":"Browning, T. D., &#38; Verzobio, M. (2025). Counting integer points on affine surfaces with a side condition. <i>Discrete Analysis</i>. Cambridge: Alliance of Diamond Open Access Journals. <a href=\"https://doi.org/10.19086/da.143787\">https://doi.org/10.19086/da.143787</a>","chicago":"Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” <i>Discrete Analysis</i>. Cambridge: Alliance of Diamond Open Access Journals, 2025. <a href=\"https://doi.org/10.19086/da.143787\">https://doi.org/10.19086/da.143787</a>.","ista":"Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12.","ieee":"T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces with a side condition,” <i>Discrete Analysis</i>, vol. 2025. Cambridge: Alliance of Diamond Open Access Journals, 2025.","ama":"Browning TD, Verzobio M. Counting integer points on affine surfaces with a side condition. <i>Discrete Analysis</i>. 2025;2025. doi:<a href=\"https://doi.org/10.19086/da.143787\">10.19086/da.143787</a>","short":"T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025)."},"arxiv":1,"oa":1,"external_id":{"arxiv":["2408.11453"]},"article_number":"12","OA_type":"diamond","project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"},{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"ddc":["510"],"intvolume":"      2025","date_created":"2026-01-18T23:02:44Z","has_accepted_license":"1","volume":2025,"ec_funded":1,"publisher":"Cambridge: Alliance of Diamond Open Access Journals","article_processing_charge":"No","type":"journal_article","acknowledgement":"Supported by FWF grant (DOI 10.55776/P36278), Supported by European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant\r\nAgreement No. 101034413."}]