[{"article_number":"e70371","publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"title":"The Davenport–Heilbronn method: 80 years on","intvolume":"       113","year":"2026","issue":"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.","type":"journal_article","language":[{"iso":"eng"}],"publication":"Journal of the London Mathematical Society","date_published":"2026-01-06T00:00:00Z","scopus_import":"1","doi":"10.1112/jlms.70371","citation":{"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).","ista":"Browning TD. 2026. The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. 113(1), e70371.","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.","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>","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>."},"OA_place":"publisher","file":[{"access_level":"open_access","file_id":"21004","relation":"main_file","creator":"dernst","date_created":"2026-01-19T08:19:46Z","checksum":"3b05bd625c81d038259a14f7e2ddd57c","success":1,"file_size":235238,"date_updated":"2026-01-19T08:19:46Z","file_name":"2026_JourLondonMathSoc_Browning.pdf","content_type":"application/pdf"}],"oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","date_created":"2026-01-18T23:02:44Z","department":[{"_id":"TiBr"}],"volume":113,"month":"01","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"}],"article_processing_charge":"Yes (via OA deal)","status":"public","project":[{"grant_number":"P36278","name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"}],"OA_type":"hybrid","day":"06","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-01-19T08:23:15Z","publisher":"Wiley","has_accepted_license":"1","ddc":["510"],"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","full_name":"Browning, Timothy D"}],"_id":"21002","oa":1,"file_date_updated":"2026-01-19T08:19:46Z","PlanS_conform":"1","corr_author":"1","quality_controlled":"1","publication_status":"published"},{"quality_controlled":"1","publication_status":"published","_id":"21242","author":[{"full_name":"Rome, Nick","last_name":"Rome","first_name":"Nick"},{"last_name":"Yamagishi","full_name":"Yamagishi, Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","first_name":"Shuntaro"}],"publisher":"Mathematical Sciences Publishers","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2406.09256","open_access":"1"}],"date_updated":"2026-02-17T11:43:14Z","page":"179-198","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"green","day":"01","external_id":{"arxiv":["2406.09256"]},"article_processing_charge":"No","month":"01","volume":340,"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"}],"department":[{"_id":"TiBr"}],"status":"public","oa_version":"Preprint","OA_place":"repository","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.","ista":"Rome N, Yamagishi S. 2026. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 340(1), 179–198.","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>.","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>","short":"N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198.","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>"},"article_type":"original","date_created":"2026-02-16T15:17:27Z","date_published":"2026-01-01T00:00:00Z","publication":"Pacific Journal of Mathematics","language":[{"iso":"eng"}],"type":"journal_article","doi":"10.2140/pjm.2026.340.179","title":"Integral solutions to systems of diagonal equations","publication_identifier":{"issn":["0030-8730"],"eissn":["1945-5844"]},"arxiv":1,"issue":"1","year":"2026","intvolume":"       340"},{"date_updated":"2026-03-02T14:05:47Z","page":"1-15","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/prm.2026.10123"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"hybrid","external_id":{"arxiv":["2411.14181"]},"project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"publication_status":"epub_ahead","PlanS_conform":"1","quality_controlled":"1","corr_author":"1","oa":1,"ddc":["510"],"has_accepted_license":"1","author":[{"orcid":"0000-0002-0704-7026","last_name":"Wang","full_name":"Wang, Victor","first_name":"Victor","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9"},{"last_name":"Xu","full_name":"Xu, Max","first_name":"Max"}],"_id":"21385","publisher":"Cambridge University Press","doi":"10.1017/prm.2026.10123","date_published":"2026-01-01T00:00:00Z","publication":"Proceedings of the Royal Society of Edinburgh: Section A Mathematics","language":[{"iso":"eng"}],"type":"journal_article","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.","year":"2026","title":"Average sizes of mixed character sums","publication_identifier":{"eissn":["1473-7124"],"issn":["0308-2105"]},"arxiv":1,"status":"public","month":"01","abstract":[{"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. ","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","department":[{"_id":"TiBr"}],"article_type":"original","ec_funded":1,"date_created":"2026-03-02T10:09:23Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"oa_version":"Published Version","citation":{"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>","short":"V. Wang, M. Xu, Proceedings of the Royal Society of Edinburgh: Section A Mathematics (2026) 1–15.","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.","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>","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>."},"OA_place":"publisher"},{"status":"public","department":[{"_id":"TiBr"}],"volume":155,"month":"10","isi":1,"abstract":[{"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.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ec_funded":1,"article_type":"original","date_created":"2023-01-16T11:45:22Z","citation":{"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.","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.","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.","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>.","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>","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>."},"OA_place":"publisher","file":[{"success":1,"checksum":"c5ec6e29aca2fb4533cb95fac409a0b2","content_type":"application/pdf","file_size":477624,"file_name":"2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf","date_updated":"2025-12-30T06:45:47Z","access_level":"open_access","date_created":"2025-12-30T06:45:47Z","creator":"dernst","relation":"main_file","file_id":"20878"}],"oa_version":"Published Version","doi":"10.1017/prm.2024.7","type":"journal_article","date_published":"2025-10-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","scopus_import":"1","intvolume":"       155","year":"2025","issue":"5","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.","arxiv":1,"publication_identifier":{"issn":["0308-2105"],"eissn":["1473-7124"]},"title":"Common valuations of division polynomials","publication_status":"published","quality_controlled":"1","corr_author":"1","PlanS_conform":"1","file_date_updated":"2025-12-30T06:45:47Z","oa":1,"publisher":"Cambridge University Press","ddc":["510"],"has_accepted_license":"1","author":[{"full_name":"Naskręcki, Bartosz","last_name":"Naskręcki","first_name":"Bartosz"},{"full_name":"Verzobio, Matteo","last_name":"Verzobio","orcid":"0000-0002-0854-0306","first_name":"Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"_id":"12311","page":"1646-1660","date_updated":"2025-12-30T06:46:17Z","OA_type":"hybrid","day":"01","external_id":{"isi":["001174907100001"],"arxiv":["2203.02015"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"keyword":["Elliptic curves","Néron models","division polynomials","height functions","discrete valuation rings"]},{"has_accepted_license":"1","ddc":["510"],"_id":"20850","author":[{"first_name":"Yijie","id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b","orcid":"0000-0002-4989-5330","last_name":"Diao","full_name":"Diao, Yijie"}],"publisher":"Université de Bordeaux","oa":1,"file_date_updated":"2025-12-29T10:05:22Z","quality_controlled":"1","corr_author":"1","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2408.03774"]},"day":"27","OA_type":"hybrid","date_updated":"2025-12-29T10:08:46Z","page":"973-988","file":[{"checksum":"67aa0afbc0b5bcbff5341f4d25e6ba20","success":1,"date_updated":"2025-12-29T10:05:22Z","file_name":"2025_JTNB_Diao.pdf","file_size":766196,"content_type":"application/pdf","access_level":"open_access","file_id":"20861","relation":"main_file","date_created":"2025-12-29T10:05:22Z","creator":"dernst"}],"oa_version":"Published Version","citation":{"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>","ista":"Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 37(3), 973–988.","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.","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>.","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>.","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>"},"OA_place":"publisher","article_type":"original","date_created":"2025-12-21T23:01:35Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)"},"volume":37,"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."},{"lang":"fre","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."}],"article_processing_charge":"Yes (in subscription journal)","department":[{"_id":"TiBr"}],"status":"public","title":"Class numbers and integer points on some Pellian surfaces","publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"arxiv":1,"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.","issue":"3","intvolume":"        37","year":"2025","language":[{"iso":"eng"}],"date_published":"2025-11-27T00:00:00Z","publication":"Journal de theorie des nombres de Bordeaux","scopus_import":"1","type":"journal_article","doi":"10.5802/jtnb.1348"},{"corr_author":"1","publication_status":"published","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","full_name":"Browning, Timothy D"},{"last_name":"Verzobio","orcid":"0000-0002-0854-0306","full_name":"Verzobio, Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","first_name":"Matteo"}],"_id":"21003","has_accepted_license":"1","ddc":["510"],"publisher":"Cambridge: Alliance of Diamond Open Access Journals","oa":1,"file_date_updated":"2026-02-12T07:50:47Z","date_updated":"2026-02-12T08:03:12Z","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"},{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","OA_type":"diamond","external_id":{"arxiv":["2408.11453"]},"article_processing_charge":"No","abstract":[{"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.","lang":"eng"}],"volume":2025,"month":"09","department":[{"_id":"TiBr"}],"status":"public","oa_version":"Published Version","file":[{"access_level":"open_access","file_id":"21214","creator":"dernst","date_created":"2026-02-12T07:50:47Z","relation":"main_file","checksum":"3d38e850b40f3e1abbfd30073bd4388a","success":1,"content_type":"application/pdf","file_size":393625,"date_updated":"2026-02-12T07:50:47Z","file_name":"2025_DiscreteAnalysis_Browning.pdf"}],"OA_place":"publisher","citation":{"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>.","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>","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>.","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.","short":"T.D. Browning, M. Verzobio, Discrete Analysis 2025 (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>"},"article_type":"original","date_created":"2026-01-18T23:02:44Z","ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"scopus_import":"1","language":[{"iso":"eng"}],"publication":"Discrete Analysis","date_published":"2025-09-01T00:00:00Z","type":"journal_article","doi":"10.19086/da.143787","title":"Counting integer points on affine surfaces with a side condition","publication_identifier":{"eissn":["2397-3129"]},"article_number":"12","arxiv":1,"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.","year":"2025","intvolume":"      2025"},{"issue":"10","acknowledgement":"We are very grateful to Tim Santens for useful conversations and to the anonymous referees for numerous pertinent remarks. While working on this paper, Browning was supported by a FWF grant (DOI 10.55776/P32428), Lyczak was supported by UKRI MR/V021362/1, and Smeets was supported by grant G0B1721N of the Fund for Scientific Research – Flanders.","intvolume":"        19","year":"2025","title":"Paucity of rational points on fibrations with multiple fibres","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"arxiv":1,"doi":"10.2140/ant.2025.19.2049","language":[{"iso":"eng"}],"date_published":"2025-09-05T00:00:00Z","publication":"Algebra & Number Theory","type":"journal_article","date_created":"2026-02-16T15:22:19Z","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"success":1,"checksum":"e50a60a4303b81563f7adbcadbe2e986","date_updated":"2026-02-17T11:56:20Z","file_size":1505580,"file_name":"2025_AlgebraNumberTheory_Browning.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2026-02-17T11:56:20Z","creator":"dernst","file_id":"21300"}],"oa_version":"Published Version","citation":{"ieee":"T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations with multiple fibres,” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10. Mathematical Sciences Publishers, pp. 2049–2090, 2025.","ista":"Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations with multiple fibres. Algebra &#38; Number Theory. 19(10), 2049–2090.","chicago":"Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>.","mla":"Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10, Mathematical Sciences Publishers, 2025, pp. 2049–90, doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>.","apa":"Browning, T. D., Lyczak, J., &#38; Smeets, A. (2025). Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>","short":"T.D. Browning, J. Lyczak, A. Smeets, Algebra &#38; Number Theory 19 (2025) 2049–2090.","ama":"Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. 2025;19(10):2049-2090. doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>"},"OA_place":"publisher","status":"public","abstract":[{"lang":"eng","text":"Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity criterion for the existence of everywhere locally soluble fibres and formulate new conjectures that generalise previous work of Loughran and Smeets. These conjectures involve geometric invariants of the associated multiplicity orbifolds on the base of the fibration in the spirit of Campana. We give evidence for the conjectures by providing an assortment of bounds using Chebotarev’s theorem and sieve methods, with most of the evidence involving upper bounds. "}],"month":"09","volume":19,"article_processing_charge":"No","department":[{"_id":"TiBr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2310.01135"]},"OA_type":"diamond","day":"05","project":[{"call_identifier":"FWF","grant_number":"P32428","name":"New frontiers of the Manin conjecture","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425"}],"date_updated":"2026-02-17T11:59:57Z","page":"2049-2090","file_date_updated":"2026-02-17T11:56:20Z","oa":1,"has_accepted_license":"1","ddc":["510"],"author":[{"first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"first_name":"Julian","last_name":"Lyczak","full_name":"Lyczak, Julian"},{"full_name":"Smeets, Arne","last_name":"Smeets","first_name":"Arne"}],"_id":"21244","publisher":"Mathematical Sciences Publishers","publication_status":"published","PlanS_conform":"1","corr_author":"1","quality_controlled":"1"},{"publication_status":"epub_ahead","quality_controlled":"1","corr_author":"1","oa":1,"publisher":"EMS Press","ddc":["500"],"author":[{"full_name":"Yao Xiao, Stanley","last_name":"Yao Xiao","first_name":"Stanley"},{"last_name":"Yamagishi","full_name":"Yamagishi, Shuntaro","first_name":"Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b"}],"_id":"21260","date_updated":"2026-06-18T18:31:24Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1697"}],"day":"06","OA_type":"diamond","external_id":{"arxiv":["2307.05712"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","call_identifier":"FWF"}],"status":"public","department":[{"_id":"TiBr"}],"abstract":[{"text":"We prove that there does not exist F∈Q[x,y] of degree 4 such that F(Z^2 )=Z ≥0. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials.","lang":"eng"}],"month":"08","article_processing_charge":"No","date_created":"2026-02-16T16:00:02Z","article_type":"original","citation":{"ama":"Yao Xiao S, Yamagishi S. Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>","short":"S. Yao Xiao, S. Yamagishi, Journal of the European Mathematical Society (2025).","apa":"Yao Xiao, S., &#38; Yamagishi, S. (2025). Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>","mla":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>.","chicago":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>.","ieee":"S. Yao Xiao and S. Yamagishi, “Quartic polynomials in two variables do not represent all non-negative integers,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","ista":"Yao Xiao S, Yamagishi S. 2025. Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society."},"OA_place":"publisher","oa_version":"Published Version","doi":"10.4171/jems/1697","type":"journal_article","date_published":"2025-08-06T00:00:00Z","language":[{"iso":"eng"}],"publication":"Journal of the European Mathematical Society","year":"2025","acknowledgement":"The first author would like to thank Samir Siksek for introducing the problem\r\nto him. The material in Section 6 is a result of discussing with many people, and the second author is very grateful to Tim Browning, Stephanie Chan, Jakob Glas, Jakub Löwit, Mirko Mauri, Marta Pieropan, Mike Roth, Matteo Verzobio and Victor Wang for taking the time to answer his questions and for their valuable suggestions. We thank Tim Browning, Yijie Diao, Ana Marija Vego and the anonymous referee for their helpful comments.\r\nThe first author was supported by NSERC Discovery Grant RGPIN-2024-06810. The\r\nsecond author was supported by the NWO Veni Grant 016.Veni.192.047 during his time at\r\nUtrecht University and by a FWF grant (DOI 10.55776/P32428) at the Institute of Science and\r\nTechnology Austria while working on this paper.","publication_identifier":{"eissn":["1435-9863"],"issn":["1435-9855"]},"arxiv":1,"title":"Quartic polynomials in two variables do not represent all non-negative integers"},{"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"day":"01","OA_type":"green","external_id":{"arxiv":["2405.04094"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.04094"}],"date_updated":"2026-02-18T07:41:56Z","publisher":"Oxford University Press","_id":"21265","author":[{"full_name":"Wang, Victor","orcid":"0000-0002-0704-7026","last_name":"Wang","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","first_name":"Victor"},{"full_name":"Xu, Max Wenqiang","last_name":"Xu","first_name":"Max Wenqiang"}],"oa":1,"quality_controlled":"1","publication_status":"published","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"article_number":"rnaf279","arxiv":1,"title":"Harper’s beyond square-root conjecture","intvolume":"      2025","year":"2025","issue":"18","acknowledgement":"The first author is supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. The second author is supported by a Simons Junior Fellowship from Simons Foundation. We thank Paul Bourgade and Kannan Soundararajan for discussions on random matrices and probability, Alexandra Florea for helpful comments on the Ratios Conjecture, and Joni Teräväinen for providing several references. We are also grateful to Alexandra Florea, Adam Harper, Joni Teräväinen, and the referee for helpful comments on earlier drafts.","type":"journal_article","date_published":"2025-09-01T00:00:00Z","publication":"International Mathematics Research Notices","language":[{"iso":"eng"}],"scopus_import":"1","doi":"10.1093/imrn/rnaf279","citation":{"chicago":"Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2025. <a href=\"https://doi.org/10.1093/imrn/rnaf279\">https://doi.org/10.1093/imrn/rnaf279</a>.","apa":"Wang, V., &#38; Xu, M. W. (2025). Harper’s beyond square-root conjecture. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnaf279\">https://doi.org/10.1093/imrn/rnaf279</a>","mla":"Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” <i>International Mathematics Research Notices</i>, vol. 2025, no. 18, rnaf279, Oxford University Press, 2025, doi:<a href=\"https://doi.org/10.1093/imrn/rnaf279\">10.1093/imrn/rnaf279</a>.","ieee":"V. Wang and M. W. Xu, “Harper’s beyond square-root conjecture,” <i>International Mathematics Research Notices</i>, vol. 2025, no. 18. Oxford University Press, 2025.","ista":"Wang V, Xu MW. 2025. Harper’s beyond square-root conjecture. International Mathematics Research Notices. 2025(18), rnaf279.","short":"V. Wang, M.W. Xu, International Mathematics Research Notices 2025 (2025).","ama":"Wang V, Xu MW. Harper’s beyond square-root conjecture. <i>International Mathematics Research Notices</i>. 2025;2025(18). doi:<a href=\"https://doi.org/10.1093/imrn/rnaf279\">10.1093/imrn/rnaf279</a>"},"OA_place":"repository","oa_version":"Preprint","ec_funded":1,"date_created":"2026-02-17T07:45:45Z","article_type":"original","department":[{"_id":"TiBr"}],"month":"09","abstract":[{"lang":"eng","text":"We explain how the (shifted) Ratios Conjecture for $L(s,\\chi )$ would extend a randomization argument of Harper from a conductor-limited range to an unlimited range of “beyond square-root cancellation” for character twists of the Liouville function. As a corollary, the Liouville function would have nontrivial cancellation in arithmetic progressions of modulus just exceeding the well-known square-root barrier. Morally, the paper passes from random matrices to random multiplicative functions."}],"volume":2025,"article_processing_charge":"No","status":"public"},{"title":"Almost all quadratic twists of an elliptic curve have no integral points","arxiv":1,"publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"acknowledgement":"The authors are grateful to Roger Heath-Brown and to the anonymous referees for useful comments. The first author was supported by an FWF grant (DOI 10.55776/P36278).","year":"2025","publication":"Journal of the European Mathematical Society","language":[{"iso":"eng"}],"date_published":"2025-09-17T00:00:00Z","type":"journal_article","doi":"10.4171/jems/1704","oa_version":"Published Version","OA_place":"publisher","citation":{"short":"T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025).","ama":"Browning TD, Chan S. Almost all quadratic twists of an elliptic curve have no integral points. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1704\">10.4171/jems/1704</a>","chicago":"Browning, Timothy D, and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press, 2025. <a href=\"https://doi.org/10.4171/jems/1704\">https://doi.org/10.4171/jems/1704</a>.","mla":"Browning, Timothy D., and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” <i>Journal of the European Mathematical Society</i>, European Mathematical Society Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1704\">10.4171/jems/1704</a>.","apa":"Browning, T. D., &#38; Chan, S. (2025). Almost all quadratic twists of an elliptic curve have no integral points. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press. <a href=\"https://doi.org/10.4171/jems/1704\">https://doi.org/10.4171/jems/1704</a>","ieee":"T. D. Browning and S. Chan, “Almost all quadratic twists of an elliptic curve have no integral points,” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press, 2025.","ista":"Browning TD, Chan S. 2025. Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society."},"date_created":"2026-02-17T07:46:26Z","article_type":"original","article_processing_charge":"No","abstract":[{"lang":"eng","text":"For a given elliptic curve E in short Weierstrass form, we show that almost all quadratic twists E \r\nD have no integral points, as D ranges over square-free integers ordered by size. Our result is conditional on a weak form of the Hall–Lang conjecture in the case that E has partial 2-torsion. The proof uses a correspondence of Mordell and the reduction theory of binary quartic forms in order to transfer the problem to counting rational points of bounded height on a certain singular cubic surface, together with extensive use of cancellation in character sum estimates, drawn from Heath-Brown’s analysis of Selmer group statistics for the congruent number curve."}],"month":"09","department":[{"_id":"TiBr"}],"status":"public","project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2401.04375"]},"OA_type":"diamond","day":"17","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1704"}],"date_updated":"2026-06-18T18:31:51Z","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-8467-4106","last_name":"Chan","full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung"}],"_id":"21266","ddc":["510"],"publisher":"European Mathematical Society Press","oa":1,"corr_author":"1","quality_controlled":"1","publication_status":"epub_ahead","DOAJ_listed":"1"},{"acknowledgement":"While working on this paper, the first author was supported by a FWF grant (DOI 10.55776/P36278).","intvolume":"        12","year":"2025","title":"Solubility of a resultant equation and applications","publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"arxiv":1,"doi":"10.5802/jep.320","date_published":"2025-10-21T00:00:00Z","language":[{"iso":"eng"}],"publication":"Journal de l'ecole polytechnique mathematiques","scopus_import":"1","type":"journal_article","article_type":"original","date_created":"2026-02-22T23:01:36Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"content_type":"application/pdf","file_size":1003689,"file_name":"2025_JEP_Browning.pdf","date_updated":"2026-02-24T07:56:34Z","checksum":"828577ea48ac6109d3e9dd1aeddd45c4","success":1,"file_id":"21356","date_created":"2026-02-24T07:56:34Z","creator":"dernst","relation":"main_file","access_level":"open_access"}],"oa_version":"Published Version","citation":{"ama":"Browning TD, Chan S. Solubility of a resultant equation and applications. <i>Journal de l’ecole polytechnique mathematiques</i>. 2025;12:1677-1691. doi:<a href=\"https://doi.org/10.5802/jep.320\">10.5802/jep.320</a>","short":"T.D. Browning, S. Chan, Journal de l’ecole Polytechnique Mathematiques 12 (2025) 1677–1691.","ista":"Browning TD, Chan S. 2025. Solubility of a resultant equation and applications. Journal de l’ecole polytechnique mathematiques. 12, 1677–1691.","ieee":"T. D. Browning and S. Chan, “Solubility of a resultant equation and applications,” <i>Journal de l’ecole polytechnique mathematiques</i>, vol. 12. Ecole polytechnique, pp. 1677–1691, 2025.","mla":"Browning, Timothy D., and Stephanie Chan. “Solubility of a Resultant Equation and Applications.” <i>Journal de l’ecole Polytechnique Mathematiques</i>, vol. 12, Ecole polytechnique, 2025, pp. 1677–91, doi:<a href=\"https://doi.org/10.5802/jep.320\">10.5802/jep.320</a>.","apa":"Browning, T. D., &#38; Chan, S. (2025). Solubility of a resultant equation and applications. <i>Journal de l’ecole Polytechnique Mathematiques</i>. Ecole polytechnique. <a href=\"https://doi.org/10.5802/jep.320\">https://doi.org/10.5802/jep.320</a>","chicago":"Browning, Timothy D, and Stephanie Chan. “Solubility of a Resultant Equation and Applications.” <i>Journal de l’ecole Polytechnique Mathematiques</i>. Ecole polytechnique, 2025. <a href=\"https://doi.org/10.5802/jep.320\">https://doi.org/10.5802/jep.320</a>."},"OA_place":"publisher","status":"public","abstract":[{"text":"The large sieve is used to estimate the density of quadratic polynomials Q ∈ Z[x],\r\nsuch that there exists an odd degree polynomial defined over Z which has resultant ±1 with Q.\r\nGiven a monic polynomial R ∈ Z[x] of odd degree, this is used to show that for almost all\r\nquadratic polynomials Q ∈ Z[x], there exists a prime p such that Q and R share a common\r\nroot in Fp. Using recent work of Landesman, an application to the average size of the odd part\r\nof the class group of quadratic number fields is also given","lang":"eng"},{"lang":"fre","text":" Le grand crible est utilisé pour estimer la densité des polynômes quadratiques Q ∈ Z[x] tels qu’il existe un polynôme de degré impair défini sur Z dont le résultant avec Q est égal à ±1. Étant donné un polynôme unitaire R ∈ Z[x] de degré impair, on s’en sert pour montrer que, pour presque tous les polynômes quadratiques Q ∈ Z[x], il existe un nombre premier p tel que Q et R aient une racine commune dans Fp. En utilisant des travaux récents de Landesman, on obtient également une application concernant la taille moyenne de la partie impaire du groupe de classe des corps quadratiques."}],"volume":12,"month":"10","article_processing_charge":"Yes","department":[{"_id":"TiBr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"21","external_id":{"arxiv":["2411.09264"]},"OA_type":"gold","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"}],"date_updated":"2026-02-24T07:57:53Z","page":"1677-1691","file_date_updated":"2026-02-24T07:56:34Z","oa":1,"ddc":["510"],"has_accepted_license":"1","author":[{"first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177"},{"orcid":"0000-0001-8467-4106","last_name":"Chan","full_name":"Chan, Yik Tung","first_name":"Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1"}],"_id":"21343","publisher":"Ecole polytechnique","DOAJ_listed":"1","publication_status":"published","PlanS_conform":"1","quality_controlled":"1","corr_author":"1"},{"_id":"21768","author":[{"full_name":"Yamagishi, Shuntaro","last_name":"Yamagishi","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","first_name":"Shuntaro"}],"publisher":"Instytut Matematyczny","oa":1,"quality_controlled":"1","corr_author":"1","publication_status":"published","keyword":["Diophantine equations","homogeneous forms"],"project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2304.02620"]},"day":"28","OA_type":"green","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2304.02620"}],"date_updated":"2026-04-28T06:31:40Z","page":"141-151","oa_version":"Preprint","citation":{"apa":"Yamagishi, S. (2025). Birch’s theorem on forms in many variables with a Hessian condition. <i>Acta Arithmetica</i>. Instytut Matematyczny. <a href=\"https://doi.org/10.4064/aa241029-19-8\">https://doi.org/10.4064/aa241029-19-8</a>","mla":"Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” <i>Acta Arithmetica</i>, vol. 221, no. 2, Instytut Matematyczny, 2025, pp. 141–51, doi:<a href=\"https://doi.org/10.4064/aa241029-19-8\">10.4064/aa241029-19-8</a>.","chicago":"Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” <i>Acta Arithmetica</i>. Instytut Matematyczny, 2025. <a href=\"https://doi.org/10.4064/aa241029-19-8\">https://doi.org/10.4064/aa241029-19-8</a>.","ista":"Yamagishi S. 2025. Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. 221(2), 141–151.","ieee":"S. Yamagishi, “Birch’s theorem on forms in many variables with a Hessian condition,” <i>Acta Arithmetica</i>, vol. 221, no. 2. Instytut Matematyczny, pp. 141–151, 2025.","ama":"Yamagishi S. Birch’s theorem on forms in many variables with a Hessian condition. <i>Acta Arithmetica</i>. 2025;221(2):141-151. doi:<a href=\"https://doi.org/10.4064/aa241029-19-8\">10.4064/aa241029-19-8</a>","short":"S. Yamagishi, Acta Arithmetica 221 (2025) 141–151."},"OA_place":"repository","article_type":"original","date_created":"2026-04-26T22:01:48Z","abstract":[{"text":"Let F∈Z[x1,…,xn] be a homogeneous form of degree d≥2, and V∗F the singular locus of the hypersurface {x∈AnC:F(x)=0}. A longstanding result of Birch states that there is a non-trivial integral solution to the equation F(x1,…,xn)=0 provided n>dimV∗F+(d−1)2d, and there is a non-singular solution in R and Qp for all primes p. We give a different formulation of this result. More precisely, we replace dimV∗F with a quantity HF defined in terms of the Hessian matrix of F. This quantity satisfies 0≤HF≤dimV∗F; therefore, we improve on the aforementioned result of Birch if HF<dimV∗F. We also prove the corresponding result for systems of forms of equal degree.","lang":"eng"}],"volume":221,"month":"10","article_processing_charge":"No","department":[{"_id":"TiBr"}],"status":"public","title":"Birch’s theorem on forms in many variables with a Hessian condition","publication_identifier":{"issn":["0065-1036"],"eissn":["1730-6264"]},"arxiv":1,"acknowledgement":"The author would like to thank Tim Browning, Jakob Glas and Simon Rydin Myerson for useful suggestions and conversations. Finally, he would like to thank the anonymous referees for their helpful comments. The author was supported by the NWO Veni Grant 016.Veni.192.047 during his time at Utrecht University and by the FWF grant P 36278 at the Institute of Science and Technology Austria while working on this article.","issue":"2","intvolume":"       221","year":"2025","publication":"Acta Arithmetica","language":[{"iso":"eng"}],"date_published":"2025-10-28T00:00:00Z","scopus_import":"1","type":"journal_article","doi":"10.4064/aa241029-19-8"},{"oa_version":"Published Version","file":[{"file_name":"2025_MathAnnalen_Glas.pdf","date_updated":"2025-04-16T09:38:55Z","file_size":650021,"content_type":"application/pdf","success":1,"checksum":"dcf57a8b01332c36e0cf2b0d1aeecb36","relation":"main_file","date_created":"2025-04-16T09:38:55Z","creator":"dernst","file_id":"19579","access_level":"open_access"}],"OA_place":"publisher","citation":{"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>.","ista":"Glas J, Hochfilzer L. 2025. On a question of Davenport and diagonal cubic forms over Fq(t). Mathematische Annalen. 391, 5485–5533.","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>"},"date_created":"2024-12-22T23:01:48Z","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","month":"04","abstract":[{"lang":"eng","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]."}],"volume":391,"isi":1,"department":[{"_id":"TiBr"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"18293"}]},"status":"public","title":"On a question of Davenport and diagonal cubic forms over Fq(t)","arxiv":1,"publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"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.","year":"2025","intvolume":"       391","scopus_import":"1","date_published":"2025-04-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"Mathematische Annalen","type":"journal_article","doi":"10.1007/s00208-024-03035-z","_id":"18705","author":[{"first_name":"Jakob","id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","last_name":"Glas","full_name":"Glas, Jakob"},{"last_name":"Hochfilzer","full_name":"Hochfilzer, Leonhard","first_name":"Leonhard"}],"ddc":["510"],"has_accepted_license":"1","publisher":"Springer Nature","oa":1,"file_date_updated":"2025-04-16T09:38:55Z","corr_author":"1","quality_controlled":"1","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","external_id":{"arxiv":["2208.05422"],"isi":["001376740400001"]},"OA_type":"hybrid","date_updated":"2025-05-19T14:04:46Z","page":"5485-5533"},{"article_processing_charge":"Yes (via OA deal)","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"}],"isi":1,"volume":71,"month":"01","department":[{"_id":"TiBr"}],"status":"public","oa_version":"Published Version","file":[{"checksum":"700a8596b4bffce2320d074120962c22","success":1,"file_name":"2025_Mathematika_Wang.pdf","file_size":309893,"date_updated":"2025-01-14T06:52:09Z","content_type":"application/pdf","access_level":"open_access","file_id":"18845","relation":"main_file","creator":"dernst","date_created":"2025-01-14T06:52:09Z"}],"OA_place":"publisher","citation":{"ista":"Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1), e70008.","ieee":"V. Wang, “Diagonal cubic forms and the large sieve,” <i>Mathematika</i>, vol. 71, no. 1. London Mathematical Society, 2025.","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>.","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>","short":"V. Wang, Mathematika 71 (2025)."},"article_type":"original","ec_funded":1,"date_created":"2025-01-12T23:04:01Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"scopus_import":"1","date_published":"2025-01-02T00:00:00Z","publication":"Mathematika","language":[{"iso":"eng"}],"type":"journal_article","doi":"10.1112/mtk.70008","title":"Diagonal cubic forms and the large sieve","publication_identifier":{"issn":["0025-5793"],"eissn":["2041-7942"]},"article_number":"e70008","issue":"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.","year":"2025","intvolume":"        71","quality_controlled":"1","corr_author":"1","publication_status":"published","author":[{"first_name":"Victor","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","orcid":"0000-0002-0704-7026","last_name":"Wang","full_name":"Wang, Victor"}],"_id":"18822","has_accepted_license":"1","ddc":["510"],"publisher":"London Mathematical Society","file_date_updated":"2025-01-14T06:52:09Z","oa":1,"date_updated":"2025-04-14T07:54:56Z","project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["001388255500001"]},"OA_type":"hybrid","day":"02"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"22","external_id":{"arxiv":["2302.07339"]},"OA_type":"diamond","project":[{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"}],"date_updated":"2026-02-17T13:19:19Z","page":"883-965","oa":1,"file_date_updated":"2026-02-17T13:17:00Z","author":[{"full_name":"Faisant, Loïs","last_name":"Faisant","first_name":"Loïs","id":"26ca6926-5797-11ee-9232-f8b51bd19631"}],"_id":"19054","ddc":["510"],"has_accepted_license":"1","publisher":"Mathematical Sciences Publishers","publication_status":"published","quality_controlled":"1","corr_author":"1","PlanS_conform":"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.","year":"2025","intvolume":"        19","title":"Motivic distribution of rational curves and twisted products of toric varieties","arxiv":1,"publication_identifier":{"eissn":["1944-7833"]},"doi":"10.2140/ant.2025.19.883","publication":"Algebra & Number Theory","language":[{"iso":"eng"}],"date_published":"2025-04-22T00:00:00Z","type":"journal_article","date_created":"2025-02-18T13:33:14Z","ec_funded":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"oa_version":"Published Version","file":[{"access_level":"open_access","relation":"main_file","date_created":"2026-02-17T13:17:00Z","creator":"dernst","file_id":"21307","success":1,"checksum":"56299f55682528a7cd0136497ce8b383","file_size":2034433,"date_updated":"2026-02-17T13:17:00Z","file_name":"2025_AlgebraNumberTheory_Faisant.pdf","content_type":"application/pdf"}],"OA_place":"publisher","citation":{"ista":"Faisant L. 2025. Motivic distribution of rational curves and twisted products of toric varieties. Algebra &#38; Number Theory. 19, 883–965.","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.","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>.","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>","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>"},"status":"public","article_processing_charge":"No","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."}],"month":"04","volume":19,"department":[{"_id":"TiBr"}]},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2502.11704"}],"date_updated":"2025-04-14T07:54:52Z","project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2502.11704"]},"day":"17","OA_type":"green","corr_author":"1","publication_status":"submitted","_id":"19055","author":[{"id":"26ca6926-5797-11ee-9232-f8b51bd19631","first_name":"Loïs","full_name":"Faisant, Loïs","last_name":"Faisant"}],"oa":1,"publication":"arXiv","language":[{"iso":"eng"}],"date_published":"2025-02-17T00:00:00Z","type":"preprint","doi":"10.48550/ARXIV.2502.11704","title":"Motivic counting of rational curves with tangency conditions via universal torsors","arxiv":1,"article_number":"2502.11704","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","year":"2025","article_processing_charge":"No","month":"02","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"}],"department":[{"_id":"TiBr"}],"status":"public","oa_version":"Preprint","OA_place":"repository","citation":{"short":"L. Faisant, ArXiv (n.d.).","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>","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>","ieee":"L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” <i>arXiv</i>. .","ista":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704."},"date_created":"2025-02-18T13:34:07Z","ec_funded":1},{"status":"public","department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (in subscription journal)","volume":273,"month":"08","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"}],"isi":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"date_created":"2025-03-09T23:01:26Z","article_type":"original","OA_place":"publisher","citation":{"short":"S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025) 1–36.","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>","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>.","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>.","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>","ista":"Chan S, Koymans P, Pagano C, Sofos E. 2025. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 273, 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. 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On the L-polynomials of curves over finite fields. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. 2025. doi:<a href=\"https://doi.org/10.1017/prm.2025.7\">10.1017/prm.2025.7</a>","short":"F. Ballini, D. Lombardo, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics (2025).","ista":"Ballini F, Lombardo D, Verzobio M. 2025. On the L-polynomials of curves over finite fields. Proceedings of the Royal Society of Edinburgh Section A: Mathematics.","ieee":"F. Ballini, D. Lombardo, and M. Verzobio, “On the L-polynomials of curves over finite fields,” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2025.","apa":"Ballini, F., Lombardo, D., &#38; Verzobio, M. (2025). On the L-polynomials of curves over finite fields. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/prm.2025.7\">https://doi.org/10.1017/prm.2025.7</a>","mla":"Ballini, Francesco, et al. “On the L-Polynomials of Curves over Finite Fields.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, Cambridge University Press, 2025, doi:<a href=\"https://doi.org/10.1017/prm.2025.7\">10.1017/prm.2025.7</a>.","chicago":"Ballini, Francesco, Davide Lombardo, and Matteo Verzobio. “On the L-Polynomials of Curves over Finite Fields.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/prm.2025.7\">https://doi.org/10.1017/prm.2025.7</a>."},"status":"public","article_processing_charge":"Yes (via OA deal)","month":"02","abstract":[{"lang":"eng","text":"We discuss, in a non-Archimedean setting, the distribution of the coefficients of L-polynomials of curves of genus g over  Fq . Among other results, this allows us to prove that the  Q-vector space spanned by such characteristic polynomials has dimension g + 1. We also state a conjecture about the Archimedean distribution of the number of rational points of curves over finite fields."}],"isi":1,"department":[{"_id":"TiBr"}],"acknowledgement":"We thank Umberto Zannier for bringing the problem to our attention, for many useful suggestions, and especially for pointing out the relevance of the equidistribution results of Katz–Sarnak, noting that they imply the case  q≫g0 of theorem 1.4. In addition, the first author would like to thank Umberto Zannier for his guidance during his undergraduate studies, on a topic that ultimately inspired much of the work in this article. We are grateful to J. Kaczorowski and A. Perelli for sharing their work [Reference Kaczorowski and Perelli28] before publication. We thank Christophe Ritzenthaler and Elisa Lorenzo García for their interesting comments on the first version of this article, Zhao Yu Ma for a comment about remark 3.12, and the anonymous referees for their helpful suggestions.","year":"2025","title":"On the L-polynomials of curves over finite fields","publication_identifier":{"issn":["0308-2105"],"eissn":["1473-7124"]},"doi":"10.1017/prm.2025.7","scopus_import":"1","date_published":"2025-02-06T00:00:00Z","publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","language":[{"iso":"eng"}],"type":"journal_article","oa":1,"author":[{"full_name":"Ballini, Francesco","last_name":"Ballini","first_name":"Francesco"},{"first_name":"Davide","full_name":"Lombardo, Davide","last_name":"Lombardo"},{"orcid":"0000-0002-0854-0306","last_name":"Verzobio","full_name":"Verzobio, Matteo","first_name":"Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"_id":"19407","ddc":["500"],"publisher":"Cambridge University Press","publication_status":"epub_ahead","quality_controlled":"1","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"isi":["001414690400001"]},"OA_type":"hybrid","day":"06","date_updated":"2026-06-18T18:15:49Z","main_file_link":[{"url":"https://doi.org/10.1017/prm.2025.7","open_access":"1"}]},{"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2403.13359","open_access":"1"}],"date_updated":"2025-05-14T11:40:24Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2403.13359"]},"day":"07","OA_type":"green","corr_author":"1","publication_status":"epub_ahead","_id":"19483","author":[{"last_name":"Chan","orcid":"0000-0001-8467-4106","full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung"},{"last_name":"Koymans","full_name":"Koymans, Peter","first_name":"Peter"},{"last_name":"Pagano","full_name":"Pagano, Carlo","first_name":"Carlo"},{"full_name":"Sofos, Efthymios","last_name":"Sofos","first_name":"Efthymios"}],"publisher":"Scuola Normale Superiore - Edizioni della Normale","oa":1,"date_published":"2025-03-07T00:00:00Z","language":[{"iso":"eng"}],"publication":"Annali della Scuola Normale Superiore di Pisa, Classe di Scienze","type":"journal_article","doi":"10.2422/2036-2145.202412_006","title":"6-torision and integral points on quartic threefolds","arxiv":1,"article_number":"18","publication_identifier":{"eissn":["2036-2145"],"issn":["0391-173X"]},"year":"2025","month":"03","abstract":[{"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.","lang":"eng"}],"article_processing_charge":"No","department":[{"_id":"TiBr"}],"status":"public","oa_version":"Preprint","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.","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.","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>.","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>.","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>"},"OA_place":"repository","date_created":"2025-04-05T10:49:27Z","article_type":"original"},{"tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png"},"ec_funded":1,"date_created":"2025-05-11T22:02:41Z","article_type":"original","citation":{"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>.","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>.","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>","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.","ista":"Wang V. 2025. Prime Hasse principles via diophantine second moments. Journal of the Association for Mathematical Research. 3(1), 1–26.","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>"},"OA_place":"publisher","file":[{"success":1,"checksum":"f9a1057d146632890466a7dc33bf625e","date_updated":"2025-05-12T10:23:26Z","file_size":1094167,"file_name":"2025_JAMR_Wang.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2025-05-12T10:23:26Z","creator":"dernst","file_id":"19682"}],"oa_version":"Published Version","status":"public","department":[{"_id":"TiBr"}],"volume":3,"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."}],"article_processing_charge":"No","intvolume":"         3","year":"2025","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","issue":"1","publication_identifier":{"eissn":["2998-4114"]},"arxiv":1,"title":"Prime Hasse principles via diophantine second moments","doi":"10.56994/JAMR.003.001.001","type":"journal_article","date_published":"2025-01-23T00:00:00Z","publication":"Journal of the Association for Mathematical Research","language":[{"iso":"eng"}],"scopus_import":"1","oa":1,"file_date_updated":"2025-05-12T10:23:26Z","publisher":"Association for Mathematical Research","has_accepted_license":"1","ddc":["510"],"author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","first_name":"Victor","orcid":"0000-0002-0704-7026","last_name":"Wang","full_name":"Wang, Victor"}],"_id":"19673","publication_status":"published","quality_controlled":"1","corr_author":"1","external_id":{"arxiv":["2304.08674"]},"OA_type":"diamond","day":"23","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","call_identifier":"H2020"}],"page":"1-26","date_updated":"2025-05-12T10:26:00Z"}]