[{"oa_version":"Published Version","_id":"21002","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278","name":"Rational curves via function field analytic number theory"}],"oa":1,"article_type":"original","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"}],"author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177"}],"department":[{"_id":"TiBr"}],"PlanS_conform":"1","date_updated":"2026-01-19T08:23:15Z","file_date_updated":"2026-01-19T08:19:46Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","success":1,"creator":"dernst","checksum":"3b05bd625c81d038259a14f7e2ddd57c","date_created":"2026-01-19T08:19:46Z","file_name":"2026_JourLondonMathSoc_Browning.pdf","date_updated":"2026-01-19T08:19:46Z","file_size":235238,"relation":"main_file","content_type":"application/pdf","file_id":"21004"}],"publication_status":"published","volume":113,"year":"2026","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_number":"e70371","intvolume":"       113","date_published":"2026-01-06T00:00:00Z","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>.","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.","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>.","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.","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>"},"article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","publication":"Journal of the London Mathematical Society","month":"01","language":[{"iso":"eng"}],"publisher":"Wiley","OA_place":"publisher","OA_type":"hybrid","issue":"1","title":"The Davenport–Heilbronn method: 80 years on","ddc":["510"],"corr_author":"1","publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"scopus_import":"1","doi":"10.1112/jlms.70371","date_created":"2026-01-18T23:02:44Z","has_accepted_license":"1","status":"public","type":"journal_article","day":"06","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."},{"date_published":"2025-05-23T00:00:00Z","citation":{"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>","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.","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>.","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>","ista":"Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 310(4), 65.","short":"T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025)."},"intvolume":"       310","article_number":"65","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"language":[{"iso":"eng"}],"publisher":"Springer Nature","OA_place":"publisher","month":"05","publication":"Mathematische Zeitschrift","article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","ddc":["510"],"corr_author":"1","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"scopus_import":"1","OA_type":"hybrid","title":"Optimal sums of three cubes in Fq[t]","issue":"4","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).","day":"23","type":"journal_article","has_accepted_license":"1","status":"public","arxiv":1,"doi":"10.1007/s00209-025-03765-z","date_created":"2025-06-03T07:30:21Z","article_type":"original","oa":1,"project":[{"grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory"},{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"_id":"19776","ec_funded":1,"oa_version":"Published Version","department":[{"_id":"TiBr"}],"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"id":"d6423cba-dc74-11ea-a0a7-ee61689ff5fb","full_name":"Glas, Jakob","last_name":"Glas","first_name":"Jakob"},{"full_name":"Wang, Victor","orcid":"0000-0002-0704-7026","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","first_name":"Victor","last_name":"Wang"}],"external_id":{"arxiv":["2408.03668 "],"isi":["001494367000001"]},"abstract":[{"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.","lang":"eng"}],"file_date_updated":"2025-06-03T08:28:14Z","date_updated":"2025-09-30T12:43:41Z","year":"2025","volume":310,"publication_status":"published","file":[{"date_updated":"2025-06-03T08:28:14Z","file_size":461622,"relation":"main_file","content_type":"application/pdf","file_id":"19782","file_name":"2025_MathZeitschrift_Browning.pdf","success":1,"creator":"dernst","checksum":"6f71e25740c28257bf89b8bf116c2b4d","date_created":"2025-06-03T08:28:14Z","access_level":"open_access"}],"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"file":[{"success":1,"creator":"dernst","checksum":"89352f1f7e8d2b367ae5f4e9bf9eb1f5","date_created":"2025-09-03T06:44:44Z","access_level":"open_access","file_size":2484757,"date_updated":"2025-09-03T06:44:44Z","relation":"main_file","file_id":"20281","content_type":"application/pdf","file_name":"2025_SelectaMathematica_Browning.pdf"}],"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","year":"2025","volume":31,"publication_status":"published","date_updated":"2025-09-30T14:29:25Z","file_date_updated":"2025-09-03T06:44:44Z","external_id":{"arxiv":["2407.16315"],"isi":["001552779800001"]},"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"first_name":"Florian Alexander","last_name":"Wilsch","orcid":"0000-0001-7302-8256","full_name":"Wilsch, Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"abstract":[{"lang":"eng","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."}],"PlanS_conform":"1","department":[{"_id":"TiBr"}],"_id":"20249","project":[{"name":"New frontiers of the Manin conjecture","call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428"},{"grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory"}],"oa_version":"Published Version","article_type":"original","oa":1,"has_accepted_license":"1","status":"public","date_created":"2025-08-31T22:01:31Z","arxiv":1,"doi":"10.1007/s00029-025-01074-1","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).","day":"01","type":"journal_article","title":"Integral points on cubic surfaces: heuristics and numerics","issue":"4","OA_type":"hybrid","scopus_import":"1","publication_identifier":{"eissn":["1420-9020"],"issn":["1022-1824"]},"ddc":["500"],"corr_author":"1","publication":"Selecta Mathematica New Series","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","OA_place":"publisher","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"09","article_number":"81","intvolume":"        31","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"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>.","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>","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.","short":"T.D. Browning, F.A. Wilsch, Selecta Mathematica New Series 31 (2025)."},"date_published":"2025-09-01T00:00:00Z"},{"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","publication":"Mathematische Annalen","month":"10","OA_place":"publisher","publisher":"Springer Nature","language":[{"iso":"eng"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"       393","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>","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.","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>.","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>.","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>","ista":"Browning TD, Sawin W, Wang V. 2025. Pairs of commuting integer matrices. Mathematische Annalen. 393, 1863–1880.","short":"T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen 393 (2025) 1863–1880."},"date_published":"2025-10-01T00:00:00Z","doi":"10.1007/s00208-025-03285-5","date_created":"2025-09-21T22:01:31Z","arxiv":1,"has_accepted_license":"1","status":"public","type":"journal_article","day":"01","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).","title":"Pairs of commuting integer matrices","OA_type":"hybrid","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"scopus_import":"1","corr_author":"1","ddc":["510"],"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"}],"external_id":{"isi":["001567740200001"],"arxiv":["2409.01920"]},"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"first_name":"Will","last_name":"Sawin","full_name":"Sawin, Will"},{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","full_name":"Wang, Victor","orcid":"0000-0002-0704-7026","last_name":"Wang","first_name":"Victor"}],"department":[{"_id":"TiBr"}],"PlanS_conform":"1","oa_version":"Published Version","project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"},{"name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020"}],"_id":"20367","ec_funded":1,"oa":1,"page":"1863–1880","article_type":"original","isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"checksum":"1e94da1a67306e03c8e0086518faf4bc","date_created":"2026-01-05T13:15:44Z","success":1,"creator":"dernst","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"20950","date_updated":"2026-01-05T13:15:44Z","file_size":337505,"file_name":"2025_MathAnnalen_Browning.pdf"}],"publication_status":"published","volume":393,"year":"2025","date_updated":"2026-01-05T13:15:53Z","file_date_updated":"2026-01-05T13:15:44Z"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_created":"2026-02-12T07:50:47Z","checksum":"3d38e850b40f3e1abbfd30073bd4388a","creator":"dernst","success":1,"access_level":"open_access","file_id":"21214","content_type":"application/pdf","relation":"main_file","file_size":393625,"date_updated":"2026-02-12T07:50:47Z","file_name":"2025_DiscreteAnalysis_Browning.pdf"}],"publication_status":"published","year":"2025","volume":2025,"date_updated":"2026-02-12T08:03:12Z","file_date_updated":"2026-02-12T07:50:47Z","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."}],"external_id":{"arxiv":["2408.11453"]},"author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","first_name":"Matteo","last_name":"Verzobio"}],"department":[{"_id":"TiBr"}],"oa_version":"Published Version","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278","name":"Rational curves via function field analytic number theory"},{"call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program"}],"_id":"21003","ec_funded":1,"oa":1,"article_type":"original","date_created":"2026-01-18T23:02:44Z","arxiv":1,"doi":"10.19086/da.143787","has_accepted_license":"1","status":"public","type":"journal_article","day":"01","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.","title":"Counting integer points on affine surfaces with a side condition","OA_type":"diamond","scopus_import":"1","publication_identifier":{"eissn":["2397-3129"]},"corr_author":"1","ddc":["510"],"article_processing_charge":"No","publication":"Discrete Analysis","month":"09","publisher":"Cambridge: Alliance of Diamond Open Access Journals","OA_place":"publisher","language":[{"iso":"eng"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_number":"12","intvolume":"      2025","citation":{"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>","ista":"Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12.","short":"T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025).","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.","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>.","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>","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>."},"date_published":"2025-09-01T00:00:00Z"},{"intvolume":"        19","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"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>.","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>","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.","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>.","short":"T.D. Browning, J. Lyczak, A. Smeets, Algebra &#38; Number Theory 19 (2025) 2049–2090.","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>","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."},"date_published":"2025-09-05T00:00:00Z","publication":"Algebra & Number Theory","quality_controlled":"1","article_processing_charge":"No","OA_place":"publisher","publisher":"Mathematical Sciences Publishers","language":[{"iso":"eng"}],"month":"09","issue":"10","title":"Paucity of rational points on fibrations with multiple fibres","OA_type":"diamond","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"corr_author":"1","ddc":["510"],"has_accepted_license":"1","status":"public","date_created":"2026-02-16T15:22:19Z","arxiv":1,"doi":"10.2140/ant.2025.19.2049","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.","type":"journal_article","day":"05","project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"_id":"21244","oa_version":"Published Version","page":"2049-2090","article_type":"original","oa":1,"external_id":{"arxiv":["2310.01135"]},"author":[{"first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Julian","last_name":"Lyczak","full_name":"Lyczak, Julian"},{"last_name":"Smeets","first_name":"Arne","full_name":"Smeets, Arne"}],"abstract":[{"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. ","lang":"eng"}],"PlanS_conform":"1","department":[{"_id":"TiBr"}],"date_updated":"2026-02-17T11:59:57Z","file_date_updated":"2026-02-17T11:56:20Z","file":[{"access_level":"open_access","success":1,"creator":"dernst","checksum":"e50a60a4303b81563f7adbcadbe2e986","date_created":"2026-02-17T11:56:20Z","file_name":"2025_AlgebraNumberTheory_Browning.pdf","file_size":1505580,"date_updated":"2026-02-17T11:56:20Z","relation":"main_file","file_id":"21300","content_type":"application/pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":19,"year":"2025","publication_status":"published"},{"arxiv":1,"doi":"10.4171/jems/1704","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1704"}],"date_created":"2026-02-17T07:46:26Z","status":"public","day":"17","type":"journal_article","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).","DOAJ_listed":"1","title":"Almost all quadratic twists of an elliptic curve have no integral points","OA_type":"diamond","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"ddc":["510"],"corr_author":"1","quality_controlled":"1","article_processing_charge":"No","publication":"Journal of the European Mathematical Society","month":"09","publisher":"European Mathematical Society Press","OA_place":"publisher","language":[{"iso":"eng"}],"citation":{"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>","ista":"Browning TD, Chan S. 2025. Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society.","short":"T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025).","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.","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>.","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>","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>."},"date_published":"2025-09-17T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"epub_ahead","year":"2025","date_updated":"2026-06-18T18:31:51Z","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."}],"external_id":{"arxiv":["2401.04375"]},"author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning"},{"id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","full_name":"Chan, Yik Tung","orcid":"0000-0001-8467-4106","last_name":"Chan","first_name":"Yik Tung"}],"department":[{"_id":"TiBr"}],"oa_version":"Published Version","project":[{"grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory"}],"_id":"21266","oa":1,"article_type":"original"},{"department":[{"_id":"TiBr"}],"PlanS_conform":"1","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."}],"author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Chan, Yik Tung","orcid":"0000-0001-8467-4106","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung","last_name":"Chan"}],"external_id":{"arxiv":["2411.09264"]},"oa":1,"page":"1677-1691","article_type":"original","oa_version":"Published Version","project":[{"name":"Rational curves via function field analytic number theory","grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3"}],"_id":"21343","publication_status":"published","volume":12,"year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_name":"2025_JEP_Browning.pdf","relation":"main_file","content_type":"application/pdf","file_id":"21356","file_size":1003689,"date_updated":"2026-02-24T07:56:34Z","access_level":"open_access","checksum":"828577ea48ac6109d3e9dd1aeddd45c4","date_created":"2026-02-24T07:56:34Z","success":1,"creator":"dernst"}],"file_date_updated":"2026-02-24T07:56:34Z","date_updated":"2026-02-24T07:57:53Z","month":"10","language":[{"iso":"eng"}],"publisher":"Ecole polytechnique","OA_place":"publisher","article_processing_charge":"Yes","quality_controlled":"1","publication":"Journal de l'ecole polytechnique mathematiques","date_published":"2025-10-21T00:00:00Z","citation":{"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>.","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.","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>","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>","ista":"Browning TD, Chan S. 2025. Solubility of a resultant equation and applications. Journal de l’ecole polytechnique mathematiques. 12, 1677–1691.","short":"T.D. Browning, S. Chan, Journal de l’ecole Polytechnique Mathematiques 12 (2025) 1677–1691."},"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"        12","day":"21","type":"journal_article","DOAJ_listed":"1","acknowledgement":"While working on this paper, the first author was supported by a FWF grant (DOI 10.55776/P36278).","arxiv":1,"date_created":"2026-02-22T23:01:36Z","doi":"10.5802/jep.320","has_accepted_license":"1","status":"public","corr_author":"1","ddc":["510"],"scopus_import":"1","publication_identifier":{"eissn":["2270-518X"],"issn":["2429-7100"]},"OA_type":"gold","title":"Solubility of a resultant equation and applications"},{"file":[{"relation":"main_file","content_type":"application/pdf","file_id":"19052","file_size":205750,"date_updated":"2025-02-18T07:56:36Z","file_name":"2024_IMRN_Browning.pdf","checksum":"b625b8adf018d2a97591813c1fc17b96","date_created":"2025-02-18T07:56:36Z","success":1,"creator":"dernst","access_level":"open_access"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"254"}]},"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":2024,"year":"2024","publication_status":"published","date_updated":"2025-09-09T12:16:45Z","file_date_updated":"2025-02-18T07:56:36Z","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D"}],"external_id":{"isi":["001196957300001"]},"abstract":[{"text":"This paper corrects an error in an earlier work of the author.","lang":"eng"}],"department":[{"_id":"TiBr"}],"_id":"19051","oa_version":"Published Version","article_type":"original","page":"10165-10168","oa":1,"status":"public","has_accepted_license":"1","date_created":"2025-02-18T07:15:50Z","doi":"10.1093/imrn/rnae066","day":"01","type":"journal_article","OA_type":"hybrid","issue":"13","title":"The polynomial sieve and equal sums of like polynomials","corr_author":"1","ddc":["510"],"scopus_import":"1","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"publication":"International Mathematics Research Notices","article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","language":[{"iso":"eng"}],"publisher":"Oxford University Press","OA_place":"publisher","month":"07","intvolume":"      2024","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_published":"2024-07-01T00:00:00Z","citation":{"mla":"Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10165–68, doi:<a href=\"https://doi.org/10.1093/imrn/rnae066\">10.1093/imrn/rnae066</a>.","chicago":"Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae066\">https://doi.org/10.1093/imrn/rnae066</a>.","ieee":"T. D. Browning, “The polynomial sieve and equal sums of like polynomials,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University Press, pp. 10165–10168, 2024.","ama":"Browning TD. The polynomial sieve and equal sums of like polynomials. <i>International Mathematics Research Notices</i>. 2024;2024(13):10165-10168. doi:<a href=\"https://doi.org/10.1093/imrn/rnae066\">10.1093/imrn/rnae066</a>","short":"T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168.","apa":"Browning, T. D. (2024). The polynomial sieve and equal sums of like polynomials. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae066\">https://doi.org/10.1093/imrn/rnae066</a>","ista":"Browning TD. 2024. The polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. 2024(13), 10165–10168."}},{"oa_version":"Published Version","_id":"15312","oa":1,"article_type":"original","page":"220-240","abstract":[{"lang":"eng","text":"The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We address this question, on average, for polynomials of arbitrary degree."}],"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Shparlinski, Igor E.","last_name":"Shparlinski","first_name":"Igor E."}],"external_id":{"isi":["001220725000001"],"arxiv":["2305.15493"]},"department":[{"_id":"TiBr"}],"date_updated":"2025-09-04T13:47:43Z","file_date_updated":"2025-01-09T09:00:02Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"file":[{"file_id":"18794","content_type":"application/pdf","relation":"main_file","file_size":394850,"date_updated":"2025-01-09T09:00:02Z","file_name":"2024_JourNumberTheory_Browning.pdf","date_created":"2025-01-09T09:00:02Z","checksum":"614032802febde0aa8e904e9a8ef99ab","creator":"dernst","success":1,"access_level":"open_access"}],"publication_status":"published","year":"2024","volume":261,"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"       261","date_published":"2024-08-01T00:00:00Z","citation":{"short":"T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240.","ista":"Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials. Journal of Number Theory. 261, 220–240.","apa":"Browning, T. D., &#38; Shparlinski, I. E. (2024). Square-free values of random polynomials. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">https://doi.org/10.1016/j.jnt.2024.02.013</a>","mla":"Browning, Timothy D., and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” <i>Journal of Number Theory</i>, vol. 261, Elsevier, 2024, pp. 220–40, doi:<a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">10.1016/j.jnt.2024.02.013</a>.","ama":"Browning TD, Shparlinski IE. Square-free values of random polynomials. <i>Journal of Number Theory</i>. 2024;261:220-240. doi:<a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">10.1016/j.jnt.2024.02.013</a>","ieee":"T. D. Browning and I. E. Shparlinski, “Square-free values of random polynomials,” <i>Journal of Number Theory</i>, vol. 261. Elsevier, pp. 220–240, 2024.","chicago":"Browning, Timothy D, and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” <i>Journal of Number Theory</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jnt.2024.02.013\">https://doi.org/10.1016/j.jnt.2024.02.013</a>."},"article_processing_charge":"No","quality_controlled":"1","publication":"Journal of Number Theory","month":"08","language":[{"iso":"eng"}],"OA_place":"publisher","publisher":"Elsevier","OA_type":"hybrid","title":"Square-free values of random polynomials","corr_author":"1","ddc":["510"],"publication_identifier":{"issn":["0022-314X"]},"scopus_import":"1","arxiv":1,"date_created":"2024-04-14T22:01:00Z","doi":"10.1016/j.jnt.2024.02.013","status":"public","has_accepted_license":"1","type":"journal_article","day":"01"},{"date_updated":"2025-09-04T13:41:19Z","file_date_updated":"2025-01-09T09:08:14Z","isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file":[{"creator":"dernst","success":1,"date_created":"2025-01-09T09:08:14Z","checksum":"5dd51531deb1e4760c38c3c0c7d5aedc","access_level":"open_access","date_updated":"2025-01-09T09:08:14Z","file_size":1019116,"content_type":"application/pdf","file_id":"18796","relation":"main_file","file_name":"2024_MathAnnalen_Bonolis.pdf"}],"publication_status":"published","volume":390,"year":"2024","oa_version":"Published Version","_id":"15337","project":[{"name":"New frontiers of the Manin conjecture","grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"oa":1,"page":"4123-4207","article_type":"original","abstract":[{"text":"We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2).","lang":"eng"}],"external_id":{"isi":["001204670500001"],"arxiv":["2204.09322"]},"author":[{"full_name":"Bonolis, Dante","id":"6A459894-5FDD-11E9-AF35-BB24E6697425","first_name":"Dante","last_name":"Bonolis"},{"first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","full_name":"Huang, Zhizhong","last_name":"Huang","first_name":"Zhizhong"}],"department":[{"_id":"TiBr"}],"title":"Density of rational points on some quadric bundle threefolds","OA_type":"hybrid","scopus_import":"1","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"corr_author":"1","ddc":["510"],"arxiv":1,"doi":"10.1007/s00208-024-02854-4","date_created":"2024-04-21T22:00:53Z","status":"public","has_accepted_license":"1","type":"journal_article","day":"01","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).The authors are grateful to Florian Wilsch for useful comments. While working on this paper the authors were supported by FWF grant P 32428.","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"       390","citation":{"ista":"Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some quadric bundle threefolds. Mathematische Annalen. 390, 4123–4207.","apa":"Bonolis, D., Browning, T. D., &#38; Huang, Z. (2024). Density of rational points on some quadric bundle threefolds. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-024-02854-4\">https://doi.org/10.1007/s00208-024-02854-4</a>","short":"D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.","ama":"Bonolis D, Browning TD, Huang Z. Density of rational points on some quadric bundle threefolds. <i>Mathematische Annalen</i>. 2024;390:4123-4207. doi:<a href=\"https://doi.org/10.1007/s00208-024-02854-4\">10.1007/s00208-024-02854-4</a>","chicago":"Bonolis, Dante, Timothy D Browning, and Zhizhong Huang. “Density of Rational Points on Some Quadric Bundle Threefolds.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00208-024-02854-4\">https://doi.org/10.1007/s00208-024-02854-4</a>.","ieee":"D. Bonolis, T. D. Browning, and Z. Huang, “Density of rational points on some quadric bundle threefolds,” <i>Mathematische Annalen</i>, vol. 390. Springer Nature, pp. 4123–4207, 2024.","mla":"Bonolis, Dante, et al. “Density of Rational Points on Some Quadric Bundle Threefolds.” <i>Mathematische Annalen</i>, vol. 390, Springer Nature, 2024, pp. 4123–207, doi:<a href=\"https://doi.org/10.1007/s00208-024-02854-4\">10.1007/s00208-024-02854-4</a>."},"date_published":"2024-11-01T00:00:00Z","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","publication":"Mathematische Annalen","month":"11","OA_place":"publisher","publisher":"Springer Nature","language":[{"iso":"eng"}]},{"OA_place":"publisher","publisher":"Cambridge University Press","language":[{"iso":"eng"}],"month":"11","publication":"Journal of the Institute of Mathematics of Jussieu","quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","citation":{"ama":"Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2024;23(6):2859-2912. doi:<a href=\"https://doi.org/10.1017/S1474748024000161\">10.1017/S1474748024000161</a>","ieee":"T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms over totally real number fields,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024.","chicago":"Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/S1474748024000161\">https://doi.org/10.1017/S1474748024000161</a>.","mla":"Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:<a href=\"https://doi.org/10.1017/S1474748024000161\">10.1017/S1474748024000161</a>.","apa":"Browning, T. D., Pierce, L. B., &#38; Schindler, D. (2024). Generalised quadratic forms over totally real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S1474748024000161\">https://doi.org/10.1017/S1474748024000161</a>","ista":"Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. 23(6), 2859–2912.","short":"T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics of Jussieu 23 (2024) 2859–2912."},"date_published":"2024-11-01T00:00:00Z","intvolume":"        23","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"acknowledgement":"The authors are grateful to Jayce Getz for asking questions that set this project in motion and to the anonymous referee for useful comments. T.B. was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for hosting research visits.","type":"journal_article","day":"01","status":"public","has_accepted_license":"1","date_created":"2024-04-21T22:00:53Z","doi":"10.1017/S1474748024000161","arxiv":1,"publication_identifier":{"eissn":["1475-3030"],"issn":["1474-7480"]},"scopus_import":"1","corr_author":"1","ddc":["510"],"issue":"6","title":"Generalised quadratic forms over totally real number fields","OA_type":"hybrid","department":[{"_id":"TiBr"}],"external_id":{"isi":["001200337400001"],"arxiv":["2212.11038"]},"author":[{"first_name":"Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Pierce, Lillian B.","last_name":"Pierce","first_name":"Lillian B."},{"first_name":"Damaris","last_name":"Schindler","full_name":"Schindler, Damaris"}],"abstract":[{"lang":"eng","text":"We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version of the Hardy–Littlewood circle method over number fields."}],"page":"2859-2912","article_type":"original","oa":1,"project":[{"name":"New frontiers of the Manin conjecture","grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"_id":"15338","oa_version":"Published Version","volume":23,"year":"2024","publication_status":"published","file":[{"creator":"dernst","success":1,"date_created":"2025-01-09T08:56:33Z","checksum":"b300541d581a71d92314df5ae8c4cc09","access_level":"open_access","file_size":690974,"date_updated":"2025-01-09T08:56:33Z","content_type":"application/pdf","file_id":"18793","relation":"main_file","file_name":"2024_JournInstMathJussieu_Browning.pdf"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"file_date_updated":"2025-01-09T08:56:33Z","date_updated":"2025-09-04T13:44:16Z"},{"quality_controlled":"1","article_processing_charge":"Yes (via OA deal)","publication":"Mathematika","month":"10","publisher":"London Mathematical Society","OA_place":"publisher","language":[{"iso":"eng"}],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"        70","article_number":"e12269","citation":{"short":"T.D. Browning, M. Verzobio, Mathematika 70 (2024).","apa":"Browning, T. D., &#38; Verzobio, M. (2024). Strong divisibility sequences and sieve methods. <i>Mathematika</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/mtk.12269\">https://doi.org/10.1112/mtk.12269</a>","ista":"Browning TD, Verzobio M. 2024. Strong divisibility sequences and sieve methods. Mathematika. 70(4), e12269.","mla":"Browning, Timothy D., and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” <i>Mathematika</i>, vol. 70, no. 4, e12269, London Mathematical Society, 2024, doi:<a href=\"https://doi.org/10.1112/mtk.12269\">10.1112/mtk.12269</a>.","ama":"Browning TD, Verzobio M. Strong divisibility sequences and sieve methods. <i>Mathematika</i>. 2024;70(4). doi:<a href=\"https://doi.org/10.1112/mtk.12269\">10.1112/mtk.12269</a>","chicago":"Browning, Timothy D, and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” <i>Mathematika</i>. London Mathematical Society, 2024. <a href=\"https://doi.org/10.1112/mtk.12269\">https://doi.org/10.1112/mtk.12269</a>.","ieee":"T. D. Browning and M. Verzobio, “Strong divisibility sequences and sieve methods,” <i>Mathematika</i>, vol. 70, no. 4. London Mathematical Society, 2024."},"date_published":"2024-10-01T00:00:00Z","date_created":"2024-07-28T22:01:08Z","doi":"10.1112/mtk.12269","status":"public","has_accepted_license":"1","day":"01","type":"journal_article","acknowledgement":"The authors are very grateful to Andrew Granville, Dimitris Koukoulopoulos, Davide Lombardo,Florian Luca, Igor Shparlinski and Joni Teräväinen for useful comments. While working on thispaper, the first author was supported by a FWF Grant (DOI 10.55776/P36278) and the secondauthor was supported by the European Union’s Horizon 2020 research and innovation programunder the Marie Skłodowska-Curie Grant Agreement Number 101034413.","title":"Strong divisibility sequences and sieve methods","issue":"4","OA_type":"hybrid","scopus_import":"1","publication_identifier":{"eissn":["2041-7942"],"issn":["0025-5793"]},"corr_author":"1","ddc":["510"],"abstract":[{"lang":"eng","text":"We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods. At the end of the paper, there is an appendix by Sandro Bettin on divisor closed sets that we use to study the density of prime terms that appear in strong divisibility sequences."}],"external_id":{"isi":["001273912800001"]},"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D"},{"first_name":"Matteo","last_name":"Verzobio","full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb"}],"department":[{"_id":"TiBr"}],"oa_version":"Published Version","_id":"17323","ec_funded":1,"project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"},{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"oa":1,"article_type":"original","isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file":[{"file_size":273006,"date_updated":"2025-01-13T11:06:25Z","file_id":"18842","content_type":"application/pdf","relation":"main_file","file_name":"2024_Mathematika_Browning.pdf","creator":"dernst","success":1,"date_created":"2025-01-13T11:06:25Z","checksum":"0b1518bdc1a901413005c19202cfa497","access_level":"open_access"}],"publication_status":"published","volume":70,"year":"2024","date_updated":"2025-09-08T08:44:11Z","file_date_updated":"2025-01-13T11:06:25Z"},{"quality_controlled":"1","article_processing_charge":"No","publication":"Annals of Mathematics","month":"05","publisher":"Princeton University","language":[{"iso":"eng"}],"intvolume":"       197","citation":{"mla":"Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>, vol. 197, no. 3, Princeton University, 2023, pp. 1115–203, doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>.","ieee":"T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” <i>Annals of Mathematics</i>, vol. 197, no. 3. Princeton University, pp. 1115–1203, 2023.","chicago":"Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” <i>Annals of Mathematics</i>. Princeton University, 2023. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>.","ama":"Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. 2023;197(3):1115-1203. doi:<a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">10.4007/annals.2023.197.3.3</a>","short":"T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203.","ista":"Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.","apa":"Browning, T. D., Boudec, P. L., &#38; Sawin, W. (2023). The Hasse principle for random Fano hypersurfaces. <i>Annals of Mathematics</i>. Princeton University. <a href=\"https://doi.org/10.4007/annals.2023.197.3.3\">https://doi.org/10.4007/annals.2023.197.3.3</a>"},"date_published":"2023-05-01T00:00:00Z","doi":"10.4007/annals.2023.197.3.3","date_created":"2020-10-19T14:28:50Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2006.02356"}],"arxiv":1,"status":"public","type":"journal_article","day":"01","title":"The Hasse principle for random Fano hypersurfaces","issue":"3","scopus_import":"1","publication_identifier":{"issn":["0003-486X"]},"corr_author":"1","abstract":[{"text":"It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces.","lang":"eng"}],"external_id":{"isi":["000966611000003"],"arxiv":["2006.02356"]},"author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Boudec, Pierre Le","last_name":"Boudec","first_name":"Pierre Le"},{"last_name":"Sawin","first_name":"Will","full_name":"Sawin, Will"}],"department":[{"_id":"TiBr"}],"oa_version":"Preprint","_id":"8682","oa":1,"page":"1115-1203","article_type":"original","isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/when-is-necessary-sufficient/"}]},"publication_status":"published","volume":197,"year":"2023","date_updated":"2024-10-21T06:01:30Z"},{"publication_identifier":{"issn":["0391-173X"],"eissn":["2036-2145"]},"scopus_import":"1","corr_author":"1","title":"Uniform bounds for rational points on hyperelliptic fibrations","issue":"1","type":"journal_article","day":"16","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2007.14182","open_access":"1"}],"date_created":"2023-05-07T22:01:04Z","doi":"10.2422/2036-2145.202010_018","status":"public","citation":{"mla":"Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” <i>Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze</i>, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della Normale, 2023, pp. 173–204, doi:<a href=\"https://doi.org/10.2422/2036-2145.202010_018\">10.2422/2036-2145.202010_018</a>.","chicago":"Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” <i>Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale, 2023. <a href=\"https://doi.org/10.2422/2036-2145.202010_018\">https://doi.org/10.2422/2036-2145.202010_018</a>.","ieee":"D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic fibrations,” <i>Annali della Scuola Normale Superiore di Pisa - Classe di Scienze</i>, vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204, 2023.","ama":"Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic fibrations. <i>Annali della Scuola Normale Superiore di Pisa - Classe di Scienze</i>. 2023;24(1):173-204. doi:<a href=\"https://doi.org/10.2422/2036-2145.202010_018\">10.2422/2036-2145.202010_018</a>","short":"D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 24 (2023) 173–204.","apa":"Bonolis, D., &#38; Browning, T. D. (2023). Uniform bounds for rational points on hyperelliptic fibrations. <i>Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale. <a href=\"https://doi.org/10.2422/2036-2145.202010_018\">https://doi.org/10.2422/2036-2145.202010_018</a>","ista":"Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 24(1), 173–204."},"date_published":"2023-02-16T00:00:00Z","intvolume":"        24","month":"02","publisher":"Scuola Normale Superiore - Edizioni della Normale","language":[{"iso":"eng"}],"quality_controlled":"1","article_processing_charge":"No","publication":"Annali della Scuola Normale Superiore di Pisa - Classe di Scienze","date_updated":"2024-10-09T21:05:05Z","publication_status":"published","volume":24,"year":"2023","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"article_type":"original","page":"173-204","oa_version":"Preprint","_id":"12916","department":[{"_id":"TiBr"}],"abstract":[{"text":"We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend on the coefficients of the polynomial defining the surface.\r\n","lang":"eng"}],"external_id":{"arxiv":["2007.14182"]},"author":[{"last_name":"Bonolis","first_name":"Dante","id":"6A459894-5FDD-11E9-AF35-BB24E6697425","full_name":"Bonolis, Dante"},{"first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}]},{"ddc":["510"],"corr_author":"1","scopus_import":"1","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"title":"Free rational curves on low degree hypersurfaces and the circle method","issue":"3","acknowledgement":"The authors are grateful to Paul Nelson, Per Salberger and Jason Starr for useful comments. While working on this paper the first author was supported by EPRSC grant EP/P026710/1. The research was partially conducted during the period the second author served as a Clay Research Fellow, and partially conducted during the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.","day":"12","type":"journal_article","has_accepted_license":"1","status":"public","arxiv":1,"date_created":"2023-05-28T22:01:02Z","doi":"10.2140/ant.2023.17.719","date_published":"2023-04-12T00:00:00Z","citation":{"chicago":"Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” <i>Algebra and Number Theory</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/ant.2023.17.719\">https://doi.org/10.2140/ant.2023.17.719</a>.","ieee":"T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces and the circle method,” <i>Algebra and Number Theory</i>, vol. 17, no. 3. Mathematical Sciences Publishers, pp. 719–748, 2023.","ama":"Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and the circle method. <i>Algebra and Number Theory</i>. 2023;17(3):719-748. doi:<a href=\"https://doi.org/10.2140/ant.2023.17.719\">10.2140/ant.2023.17.719</a>","mla":"Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” <i>Algebra and Number Theory</i>, vol. 17, no. 3, Mathematical Sciences Publishers, 2023, pp. 719–48, doi:<a href=\"https://doi.org/10.2140/ant.2023.17.719\">10.2140/ant.2023.17.719</a>.","apa":"Browning, T. D., &#38; Sawin, W. (2023). Free rational curves on low degree hypersurfaces and the circle method. <i>Algebra and Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2023.17.719\">https://doi.org/10.2140/ant.2023.17.719</a>","ista":"Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 17(3), 719–748.","short":"T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748."},"intvolume":"        17","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"language":[{"iso":"eng"}],"publisher":"Mathematical Sciences Publishers","month":"04","publication":"Algebra and Number Theory","article_processing_charge":"No","quality_controlled":"1","file_date_updated":"2023-05-30T08:05:22Z","date_updated":"2025-04-14T09:25:44Z","volume":17,"year":"2023","publication_status":"published","file":[{"file_size":1430719,"date_updated":"2023-05-30T08:05:22Z","file_id":"13101","content_type":"application/pdf","relation":"main_file","file_name":"2023_AlgebraNumberTheory_Browning.pdf","creator":"dernst","success":1,"date_created":"2023-05-30T08:05:22Z","checksum":"5d5d67b235905650e33cf7065d7583b4","access_level":"open_access"}],"isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"719-748","article_type":"original","oa":1,"_id":"13091","project":[{"grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425","name":"Between rational and integral points"}],"oa_version":"Published Version","department":[{"_id":"TiBr"}],"author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Sawin, Will","last_name":"Sawin","first_name":"Will"}],"external_id":{"isi":["000996014700004"],"arxiv":["1810.06882"]},"abstract":[{"text":"We use a function field version of the Hardy–Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low degree. On the one hand this allows us to bound the dimension of the singular locus of the moduli space of rational curves on such hypersurfaces and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin conjecture in terms of slopes with respect to the tangent bundle.","lang":"eng"}]},{"citation":{"apa":"Browning, T. D., Lyczak, J., &#38; Sarapin, R. (2023). Local solubility for a family of quadrics over a split quadric surface. <i>Involve</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/involve.2023.16.331\">https://doi.org/10.2140/involve.2023.16.331</a>","ista":"Browning TD, Lyczak J, Sarapin R. 2023. Local solubility for a family of quadrics over a split quadric surface. Involve. 16(2), 331–342.","short":"T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 331–342.","ama":"Browning TD, Lyczak J, Sarapin R. Local solubility for a family of quadrics over a split quadric surface. <i>Involve</i>. 2023;16(2):331-342. doi:<a href=\"https://doi.org/10.2140/involve.2023.16.331\">10.2140/involve.2023.16.331</a>","ieee":"T. D. Browning, J. Lyczak, and R. Sarapin, “Local solubility for a family of quadrics over a split quadric surface,” <i>Involve</i>, vol. 16, no. 2. Mathematical Sciences Publishers, pp. 331–342, 2023.","chicago":"Browning, Timothy D, Julian Lyczak, and Roman Sarapin. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” <i>Involve</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/involve.2023.16.331\">https://doi.org/10.2140/involve.2023.16.331</a>.","mla":"Browning, Timothy D., et al. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” <i>Involve</i>, vol. 16, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–42, doi:<a href=\"https://doi.org/10.2140/involve.2023.16.331\">10.2140/involve.2023.16.331</a>."},"date_published":"2023-05-26T00:00:00Z","intvolume":"        16","publisher":"Mathematical Sciences Publishers","language":[{"iso":"eng"}],"month":"05","publication":"Involve","quality_controlled":"1","article_processing_charge":"No","publication_identifier":{"eissn":["1944-4184"],"issn":["1944-4176"]},"scopus_import":"1","corr_author":"1","issue":"2","title":"Local solubility for a family of quadrics over a split quadric surface","type":"journal_article","day":"26","status":"public","date_created":"2023-07-02T22:00:43Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2203.06881"}],"arxiv":1,"doi":"10.2140/involve.2023.16.331","page":"331-342","article_type":"original","oa":1,"_id":"13180","oa_version":"Preprint","department":[{"_id":"TiBr"}],"external_id":{"arxiv":["2203.06881"]},"author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"first_name":"Julian","last_name":"Lyczak","full_name":"Lyczak, Julian","id":"3572849A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Sarapin, Roman","first_name":"Roman","last_name":"Sarapin"}],"abstract":[{"text":"We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface","lang":"eng"}],"date_updated":"2024-10-09T21:05:51Z","volume":16,"year":"2023","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","volume":16,"year":"2022","publication_status":"published","date_updated":"2025-04-14T09:25:44Z","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"first_name":"Tal","last_name":"Horesh","full_name":"Horesh, Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425"},{"last_name":"Wilsch","first_name":"Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425","full_name":"Wilsch, Florian Alexander","orcid":"0000-0001-7302-8256"}],"external_id":{"arxiv":["2102.11552"],"isi":["000961514100004"]},"abstract":[{"lang":"eng","text":"We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre's programme on \"freeness\" for rational points of bounded height on Fano\r\nvarieties."}],"department":[{"_id":"TiBr"}],"_id":"9199","project":[{"name":"Between rational and integral points","grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","name":"New frontiers of the Manin conjecture"}],"oa_version":"Preprint","page":"2385-2407","article_type":"original","oa":1,"status":"public","date_created":"2021-02-25T09:56:57Z","doi":"10.2140/ant.2022.16.2385","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2102.11552"}],"acknowledgement":"The authors are very grateful to Will Sawin for useful remarks about this topic. While working on this paper the first two authors were supported by EPSRC grant EP/P026710/1, and the first and last authors by FWF grant P 32428-N35.","type":"journal_article","day":"01","issue":"10","title":"Equidistribution and freeness on Grassmannians","corr_author":"1","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"scopus_import":"1","publication":"Algebra & Number Theory","article_processing_charge":"No","quality_controlled":"1","language":[{"iso":"eng"}],"publisher":"Mathematical Sciences Publishers","month":"12","intvolume":"        16","date_published":"2022-12-01T00:00:00Z","citation":{"ista":"Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians. Algebra &#38; Number Theory. 16(10), 2385–2407.","apa":"Browning, T. D., Horesh, T., &#38; Wilsch, F. A. (2022). Equidistribution and freeness on Grassmannians. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2022.16.2385\">https://doi.org/10.2140/ant.2022.16.2385</a>","short":"T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &#38; Number Theory 16 (2022) 2385–2407.","ieee":"T. D. Browning, T. Horesh, and F. A. Wilsch, “Equidistribution and freeness on Grassmannians,” <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10. Mathematical Sciences Publishers, pp. 2385–2407, 2022.","chicago":"Browning, Timothy D, Tal Horesh, and Florian Alexander Wilsch. “Equidistribution and Freeness on Grassmannians.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2022. <a href=\"https://doi.org/10.2140/ant.2022.16.2385\">https://doi.org/10.2140/ant.2022.16.2385</a>.","ama":"Browning TD, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians. <i>Algebra &#38; Number Theory</i>. 2022;16(10):2385-2407. doi:<a href=\"https://doi.org/10.2140/ant.2022.16.2385\">10.2140/ant.2022.16.2385</a>","mla":"Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.” <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10, Mathematical Sciences Publishers, 2022, pp. 2385–407, doi:<a href=\"https://doi.org/10.2140/ant.2022.16.2385\">10.2140/ant.2022.16.2385</a>."}},{"status":"public","has_accepted_license":"1","date_created":"2023-03-28T09:21:09Z","acknowledgement":"This work was begun while the author was participating in the programme on \"Diophantine equations\" at the Hausdorff Research Institute for Mathematics in Bonn in 2009. The hospitality and financial support of the institute is gratefully acknowledged. The idea of using conic bundles to study the split del Pezzo surface of degree 5 was explained to the author by Professor Salberger. The author is very grateful to him for his input into this project and also to Shuntaro Yamagishi for many useful comments on an earlier version of this manuscript. While working on this paper the author was supported by FWF grant P32428-N35.","type":"journal_article","day":"24","title":"Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5","publication_identifier":{"issn":["1076-9803"]},"ddc":["510"],"corr_author":"1","publication":"New York Journal of Mathematics","quality_controlled":"1","article_processing_charge":"No","publisher":"State University of New York","language":[{"iso":"eng"}],"month":"08","intvolume":"        28","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"ista":"Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229.","apa":"Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. <i>New York Journal of Mathematics</i>. State University of New York.","short":"T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229.","ama":"Browning TD. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. <i>New York Journal of Mathematics</i>. 2022;28:1193-1229.","ieee":"T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5,” <i>New York Journal of Mathematics</i>, vol. 28. State University of New York, pp. 1193–1229, 2022.","chicago":"Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>. State University of New York, 2022.","mla":"Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” <i>New York Journal of Mathematics</i>, vol. 28, State University of New York, 2022, pp. 1193–229."},"date_published":"2022-08-24T00:00:00Z","file":[{"content_type":"application/pdf","file_id":"12778","relation":"main_file","file_size":897267,"date_updated":"2023-03-30T07:09:35Z","file_name":"2022_NYJM_Browning.pdf","date_created":"2023-03-30T07:09:35Z","checksum":"c01e8291794a1bdb7416aa103cb68ef8","creator":"dernst","success":1,"access_level":"open_access"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":28,"year":"2022","publication_status":"published","date_updated":"2025-04-15T07:39:01Z","file_date_updated":"2023-03-30T07:09:35Z","author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"}],"abstract":[{"text":"An improved asymptotic formula is established for the number of rational points of bounded height on the split smooth del Pezzo surface of degree 5. The proof uses the five conic bundle structures on the surface.","lang":"eng"}],"department":[{"_id":"TiBr"}],"project":[{"name":"New frontiers of the Manin conjecture","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","call_identifier":"FWF"}],"_id":"12776","oa_version":"Published Version","article_type":"original","page":"1193 - 1229","oa":1},{"oa":1,"page":"147-165","article_type":"original","oa_version":"Preprint","_id":"8742","project":[{"name":"New frontiers of the Manin conjecture","call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428"}],"department":[{"_id":"TiBr"}],"abstract":[{"lang":"eng","text":"We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros."}],"external_id":{"arxiv":["2003.09593"],"isi":["000604750900008"]},"author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D"},{"full_name":"Heath-Brown, Roger","last_name":"Heath-Brown","first_name":"Roger"}],"date_updated":"2025-04-15T07:39:01Z","publication_status":"published","volume":33,"year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"citation":{"ista":"Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum Mathematicum. 33(1), 147–165.","apa":"Browning, T. D., &#38; Heath-Brown, R. (2021). The geometric sieve for quadrics. <i>Forum Mathematicum</i>. De Gruyter. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>","short":"T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165.","ama":"Browning TD, Heath-Brown R. The geometric sieve for quadrics. <i>Forum Mathematicum</i>. 2021;33(1):147-165. doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>","chicago":"Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>. De Gruyter, 2021. <a href=\"https://doi.org/10.1515/forum-2020-0074\">https://doi.org/10.1515/forum-2020-0074</a>.","ieee":"T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” <i>Forum Mathematicum</i>, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021.","mla":"Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” <i>Forum Mathematicum</i>, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:<a href=\"https://doi.org/10.1515/forum-2020-0074\">10.1515/forum-2020-0074</a>."},"date_published":"2021-01-01T00:00:00Z","intvolume":"        33","month":"01","publisher":"De Gruyter","language":[{"iso":"eng"}],"quality_controlled":"1","article_processing_charge":"No","publication":"Forum Mathematicum","scopus_import":"1","publication_identifier":{"eissn":["1435-5337"],"issn":["0933-7741"]},"title":"The geometric sieve for quadrics","issue":"1","day":"01","type":"journal_article","doi":"10.1515/forum-2020-0074","date_created":"2020-11-08T23:01:25Z","arxiv":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2003.09593"}],"status":"public"}]