--- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '21002' abstract: - lang: eng 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. acknowledgement: "The author is very grateful to Jörg Brüdern, Simon Rydin Myerson and Trevor Wooley for their help and advice with preparing this survey, in addition to Vinay Kumaraswamy, Victor Wang and the anonymous referee for useful comments on an earlier draft. This work was supported by a FWF Grant (DOI 10.55776/P36278).\r\nOpen Access funding provided by Institute of Science and Technology Austria/KEMÖ." article_number: e70371 article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 citation: ama: 'Browning TD. The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. 2026;113(1). doi:10.1112/jlms.70371' apa: 'Browning, T. D. (2026). The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.70371' chicago: 'Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” Journal of the London Mathematical Society. Wiley, 2026. https://doi.org/10.1112/jlms.70371.' ieee: 'T. D. Browning, “The Davenport–Heilbronn method: 80 years on,” Journal of the London Mathematical Society, vol. 113, no. 1. Wiley, 2026.' ista: 'Browning TD. 2026. The Davenport–Heilbronn method: 80 years on. Journal of the London Mathematical Society. 113(1), e70371.' mla: 'Browning, Timothy D. “The Davenport–Heilbronn Method: 80 Years On.” Journal of the London Mathematical Society, vol. 113, no. 1, e70371, Wiley, 2026, doi:10.1112/jlms.70371.' short: T.D. Browning, Journal of the London Mathematical Society 113 (2026). corr_author: '1' das_tickbox: '0' date_created: 2026-01-18T23:02:44Z date_published: 2026-01-06T00:00:00Z date_updated: 2026-07-16T08:33:56Z day: '06' ddc: - '510' department: - _id: TiBr doi: 10.1112/jlms.70371 file: - access_level: open_access checksum: 3b05bd625c81d038259a14f7e2ddd57c content_type: application/pdf creator: dernst date_created: 2026-01-19T08:19:46Z date_updated: 2026-01-19T08:19:46Z file_id: '21004' file_name: 2026_JourLondonMathSoc_Browning.pdf file_size: 235238 relation: main_file success: 1 file_date_updated: 2026-01-19T08:19:46Z has_accepted_license: '1' intvolume: ' 113' issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 issn: - 0024-6107 publication_status: published publisher: Wiley quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: 'The Davenport–Heilbronn method: 80 years on' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 113 year: '2026' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '21385' abstract: - lang: eng text: 'We prove that the average size of a mixed character sum (math. formular) (for a suitable smooth function w) is on the order of √x for all irrational real θ satisfying a weak Diophantine condition, where χ is drawn from the family of Dirichlet characters modulo a large prime r and where x 6 r. In contrast, it was proved by Harper that the average size is o(√x) for rational θ. Certain quadratic Diophantine equations play a key role in the present paper. ' 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." article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 - first_name: Max full_name: Xu, Max last_name: Xu citation: ama: 'Wang V, Xu M. Average sizes of mixed character sums. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2026:1-15. doi:10.1017/prm.2026.10123' apa: 'Wang, V., & Xu, M. (2026). Average sizes of mixed character sums. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. Cambridge University Press. https://doi.org/10.1017/prm.2026.10123' chicago: 'Wang, Victor, and Max Xu. “Average Sizes of Mixed Character Sums.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics. Cambridge University Press, 2026. https://doi.org/10.1017/prm.2026.10123.' ieee: 'V. Wang and M. Xu, “Average sizes of mixed character sums,” Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 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.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University Press, 2026, pp. 1–15, doi:10.1017/prm.2026.10123.' short: 'V. Wang, M. Xu, Proceedings of the Royal Society of Edinburgh: Section A Mathematics (2026) 1–15.' corr_author: '1' das_tickbox: '0' date_created: 2026-03-02T10:09:23Z date_published: 2026-01-01T00:00:00Z date_updated: 2026-07-16T08:39:57Z ddc: - '510' department: - _id: TiBr doi: 10.1017/prm.2026.10123 ec_funded: 1 external_id: arxiv: - '2411.14181' has_accepted_license: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1017/prm.2026.10123 month: '01' oa: 1 oa_version: Published Version page: 1-15 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: 'Proceedings of the Royal Society of Edinburgh: Section A Mathematics' publication_identifier: eissn: - 1473-7124 issn: - 0308-2105 publication_status: epub_ahead publisher: Cambridge University Press quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Average sizes of mixed character sums tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2026' ... --- OA_place: repository OA_type: green _id: '21242' abstract: - lang: eng 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Nick full_name: Rome, Nick last_name: Rome - first_name: Shuntaro full_name: Yamagishi, Shuntaro id: 0c3fbc5c-f7a6-11ec-8d70-9485e75b416b last_name: Yamagishi citation: ama: Rome N, Yamagishi S. Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. 2026;340(1):179-198. doi:10.2140/pjm.2026.340.179 apa: Rome, N., & Yamagishi, S. (2026). Integral solutions to systems of diagonal equations. Pacific Journal of Mathematics. Mathematical Sciences Publishers. https://doi.org/10.2140/pjm.2026.340.179 chicago: Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” Pacific Journal of Mathematics. Mathematical Sciences Publishers, 2026. https://doi.org/10.2140/pjm.2026.340.179. ieee: N. Rome and S. Yamagishi, “Integral solutions to systems of diagonal equations,” Pacific Journal of Mathematics, 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. mla: Rome, Nick, and Shuntaro Yamagishi. “Integral Solutions to Systems of Diagonal Equations.” Pacific Journal of Mathematics, vol. 340, no. 1, Mathematical Sciences Publishers, 2026, pp. 179–98, doi:10.2140/pjm.2026.340.179. short: N. Rome, S. Yamagishi, Pacific Journal of Mathematics 340 (2026) 179–198. das_tickbox: '0' date_created: 2026-02-16T15:17:27Z date_published: 2026-01-01T00:00:00Z date_updated: 2026-07-16T08:36:20Z day: '01' department: - _id: TiBr doi: 10.2140/pjm.2026.340.179 external_id: arxiv: - '2406.09256' intvolume: ' 340' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2406.09256 month: '01' oa: 1 oa_version: Preprint page: 179-198 publication: Pacific Journal of Mathematics publication_identifier: eissn: - 1945-5844 issn: - 0030-8730 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Integral solutions to systems of diagonal equations type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 340 year: '2026' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20078' abstract: - lang: eng text: 'Let A be an abelian variety defined over a number field K, E/K be an elliptic curve, and ϕ : A → Em be an isogeny defined over K. Let P ∈ A(K) be such that ϕ(P)=(Q1,..., Qm) with RankZ(⟨Q1,...,Qm⟩)=1. We will study a divisibility sequence related to the point P and show its relation with elliptic divisibility sequences.' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Stefan full_name: Barańczuk, Stefan last_name: Barańczuk - first_name: Bartosz full_name: Naskręcki, Bartosz last_name: Naskręcki - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: ama: Barańczuk S, Naskręcki B, Verzobio M. Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve. Journal of Number Theory. 2026;279:170-183. doi:10.1016/j.jnt.2025.06.001 apa: Barańczuk, S., Naskręcki, B., & Verzobio, M. (2026). Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2025.06.001 chicago: Barańczuk, Stefan, Bartosz Naskręcki, and Matteo Verzobio. “Divisibility Sequences Related to Abelian Varieties Isogenous to a Power of an Elliptic Curve.” Journal of Number Theory. Elsevier, 2026. https://doi.org/10.1016/j.jnt.2025.06.001. ieee: S. Barańczuk, B. Naskręcki, and M. Verzobio, “Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve,” Journal of Number Theory, vol. 279. Elsevier, pp. 170–183, 2026. ista: Barańczuk S, Naskręcki B, Verzobio M. 2026. Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve. Journal of Number Theory. 279, 170–183. mla: Barańczuk, Stefan, et al. “Divisibility Sequences Related to Abelian Varieties Isogenous to a Power of an Elliptic Curve.” Journal of Number Theory, vol. 279, Elsevier, 2026, pp. 170–83, doi:10.1016/j.jnt.2025.06.001. short: S. Barańczuk, B. Naskręcki, M. Verzobio, Journal of Number Theory 279 (2026) 170–183. corr_author: '1' das_tickbox: '1' dataavailabilitystatement: No data was used for the research described in the article. date_created: 2025-07-27T22:01:25Z date_published: 2026-02-01T00:00:00Z date_updated: 2026-07-23T11:33:57Z day: '01' ddc: - '500' department: - _id: TiBr doi: 10.1016/j.jnt.2025.06.001 external_id: arxiv: - '2309.09699' isi: - '001541172400002' file: - access_level: open_access checksum: 34e6e965a2b30a258e0d4103350a68fd content_type: application/pdf creator: dernst date_created: 2026-07-23T11:32:51Z date_updated: 2026-07-23T11:32:51Z file_id: '22396' file_name: 2026_JourNumberTheory_Baranczuk.pdf file_size: 754810 relation: main_file success: 1 file_date_updated: 2026-07-23T11:32:51Z has_accepted_license: '1' intvolume: ' 279' isi: 1 keyword: - Divisibility sequences - Abelian varieties - Elliptic divisibility sequences - Isogenies - Primitive divisors language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 170-183 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 279 year: '2026' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '12311' abstract: - lang: eng text: In this note, we prove a formula for the cancellation exponent kv,n between division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points on an elliptic curve E defined over a discrete valuation field K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields. 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. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Bartosz full_name: Naskręcki, Bartosz last_name: Naskręcki - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: ama: 'Naskręcki B, Verzobio M. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2025;155(5):1646-1660. doi:10.1017/prm.2024.7' apa: 'Naskręcki, B., & Verzobio, M. (2025). Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge University Press. https://doi.org/10.1017/prm.2024.7' chicago: 'Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge University Press, 2025. https://doi.org/10.1017/prm.2024.7.' ieee: 'B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 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.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:10.1017/prm.2024.7.' short: 'B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 155 (2025) 1646–1660.' corr_author: '1' das_tickbox: '0' date_created: 2023-01-16T11:45:22Z date_published: 2025-10-01T00:00:00Z date_updated: 2026-07-16T08:43:40Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1017/prm.2024.7 ec_funded: 1 external_id: arxiv: - '2203.02015' isi: - '001174907100001' file: - access_level: open_access checksum: c5ec6e29aca2fb4533cb95fac409a0b2 content_type: application/pdf creator: dernst date_created: 2025-12-30T06:45:47Z date_updated: 2025-12-30T06:45:47Z file_id: '20878' file_name: 2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf file_size: 477624 relation: main_file success: 1 file_date_updated: 2025-12-30T06:45:47Z has_accepted_license: '1' intvolume: ' 155' isi: 1 issue: '5' keyword: - Elliptic curves - Néron models - division polynomials - height functions - discrete valuation rings language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1646-1660 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: 'Proceedings of the Royal Society of Edinburgh Section A: Mathematics' publication_identifier: eissn: - 1473-7124 issn: - 0308-2105 publication_status: published publisher: Cambridge University Press quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Common valuations of division polynomials tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 155 year: '2025' ... --- OA_place: publisher OA_type: diamond PlanS_conform: '1' _id: '21244' 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. ' 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Julian full_name: Lyczak, Julian last_name: Lyczak - first_name: Arne full_name: Smeets, Arne last_name: Smeets citation: ama: Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with multiple fibres. Algebra & Number Theory. 2025;19(10):2049-2090. doi:10.2140/ant.2025.19.2049 apa: Browning, T. D., Lyczak, J., & Smeets, A. (2025). Paucity of rational points on fibrations with multiple fibres. Algebra & Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2025.19.2049 chicago: Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational Points on Fibrations with Multiple Fibres.” Algebra & Number Theory. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/ant.2025.19.2049. ieee: T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations with multiple fibres,” Algebra & Number Theory, 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 & Number Theory. 19(10), 2049–2090. mla: Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with Multiple Fibres.” Algebra & Number Theory, vol. 19, no. 10, Mathematical Sciences Publishers, 2025, pp. 2049–90, doi:10.2140/ant.2025.19.2049. short: T.D. Browning, J. Lyczak, A. Smeets, Algebra & Number Theory 19 (2025) 2049–2090. corr_author: '1' das_tickbox: '0' date_created: 2026-02-16T15:22:19Z date_published: 2025-09-05T00:00:00Z date_updated: 2026-07-16T08:52:36Z day: '05' ddc: - '510' department: - _id: TiBr doi: 10.2140/ant.2025.19.2049 external_id: arxiv: - '2310.01135' file: - access_level: open_access checksum: e50a60a4303b81563f7adbcadbe2e986 content_type: application/pdf creator: dernst date_created: 2026-02-17T11:56:20Z date_updated: 2026-02-17T11:56:20Z file_id: '21300' file_name: 2025_AlgebraNumberTheory_Browning.pdf file_size: 1505580 relation: main_file success: 1 file_date_updated: 2026-02-17T11:56:20Z has_accepted_license: '1' intvolume: ' 19' issue: '10' language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 2049-2090 project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Algebra & Number Theory publication_identifier: eissn: - 1944-7833 issn: - 1937-0652 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Paucity of rational points on fibrations with multiple fibres tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 19 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '20850' 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." 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. article_processing_charge: Yes (in subscription journal) article_type: original arxiv: 1 author: - first_name: Yijie full_name: Diao, Yijie id: 7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b last_name: Diao orcid: 0000-0002-4989-5330 citation: ama: Diao Y. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 2025;37(3):973-988. doi:10.5802/jtnb.1348 apa: Diao, Y. (2025). Class numbers and integer points on some Pellian surfaces. Journal de Theorie Des Nombres de Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.1348 chicago: Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” Journal de Theorie Des Nombres de Bordeaux. Université de Bordeaux, 2025. https://doi.org/10.5802/jtnb.1348. ieee: Y. Diao, “Class numbers and integer points on some Pellian surfaces,” Journal de theorie des nombres de Bordeaux, vol. 37, no. 3. Université de Bordeaux, pp. 973–988, 2025. ista: Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 37(3), 973–988. mla: Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” Journal de Theorie Des Nombres de Bordeaux, vol. 37, no. 3, Université de Bordeaux, 2025, pp. 973–88, doi:10.5802/jtnb.1348. short: Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988. corr_author: '1' das_tickbox: '0' date_created: 2025-12-21T23:01:35Z date_published: 2025-11-27T00:00:00Z date_updated: 2026-07-16T08:45:12Z day: '27' ddc: - '510' department: - _id: TiBr doi: 10.5802/jtnb.1348 external_id: arxiv: - '2408.03774' file: - access_level: open_access checksum: 67aa0afbc0b5bcbff5341f4d25e6ba20 content_type: application/pdf creator: dernst date_created: 2025-12-29T10:05:22Z date_updated: 2025-12-29T10:05:22Z file_id: '20861' file_name: 2025_JTNB_Diao.pdf file_size: 766196 relation: main_file success: 1 file_date_updated: 2025-12-29T10:05:22Z has_accepted_license: '1' intvolume: ' 37' issue: '3' language: - iso: eng license: https://creativecommons.org/licenses/by-nd/4.0/ month: '11' oa: 1 oa_version: Published Version page: 973-988 publication: Journal de theorie des nombres de Bordeaux publication_identifier: eissn: - 2118-8572 issn: - 1246-7405 publication_status: published publisher: Université de Bordeaux quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Class numbers and integer points on some Pellian surfaces tmp: image: /image/cc_by_nd.png legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0) short: CC BY-ND (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 37 year: '2025' ... --- OA_place: publisher OA_type: diamond _id: '21003' 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. 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." article_number: '12' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: ama: Browning TD, Verzobio M. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025;2025. doi:10.19086/da.143787 apa: 'Browning, T. D., & Verzobio, M. (2025). Counting integer points on affine surfaces with a side condition. Discrete Analysis. Cambridge: Alliance of Diamond Open Access Journals. https://doi.org/10.19086/da.143787' chicago: 'Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” Discrete Analysis. Cambridge: Alliance of Diamond Open Access Journals, 2025. https://doi.org/10.19086/da.143787.' ieee: 'T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces with a side condition,” Discrete Analysis, vol. 2025. Cambridge: Alliance of Diamond Open Access Journals, 2025.' ista: Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12. mla: 'Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” Discrete Analysis, vol. 2025, 12, Cambridge: Alliance of Diamond Open Access Journals, 2025, doi:10.19086/da.143787.' short: T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025). corr_author: '1' das_tickbox: '0' date_created: 2026-01-18T23:02:44Z date_published: 2025-09-01T00:00:00Z date_updated: 2026-07-16T08:48:35Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.19086/da.143787 ec_funded: 1 external_id: arxiv: - '2408.11453' file: - access_level: open_access checksum: 3d38e850b40f3e1abbfd30073bd4388a content_type: application/pdf creator: dernst date_created: 2026-02-12T07:50:47Z date_updated: 2026-02-12T07:50:47Z file_id: '21214' file_name: 2025_DiscreteAnalysis_Browning.pdf file_size: 393625 relation: main_file success: 1 file_date_updated: 2026-02-12T07:50:47Z has_accepted_license: '1' intvolume: ' 2025' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Discrete Analysis publication_identifier: eissn: - 2397-3129 publication_status: published publisher: 'Cambridge: Alliance of Diamond Open Access Journals' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Counting integer points on affine surfaces with a side condition tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 2025 year: '2025' ... --- OA_place: publisher OA_type: diamond _id: '21260' abstract: - lang: eng 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. 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." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Stanley full_name: Yao Xiao, Stanley last_name: Yao Xiao - first_name: Shuntaro full_name: Yamagishi, Shuntaro id: 0c3fbc5c-f7a6-11ec-8d70-9485e75b416b last_name: Yamagishi citation: ama: Yao Xiao S, Yamagishi S. Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society. 2025. doi:10.4171/jems/1697 apa: Yao Xiao, S., & Yamagishi, S. (2025). Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society. EMS Press. https://doi.org/10.4171/jems/1697 chicago: Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” Journal of the European Mathematical Society. EMS Press, 2025. https://doi.org/10.4171/jems/1697. ieee: S. Yao Xiao and S. Yamagishi, “Quartic polynomials in two variables do not represent all non-negative integers,” Journal of the European Mathematical Society. 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. mla: Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” Journal of the European Mathematical Society, EMS Press, 2025, doi:10.4171/jems/1697. short: S. Yao Xiao, S. Yamagishi, Journal of the European Mathematical Society (2025). corr_author: '1' das_tickbox: '0' date_created: 2026-02-16T16:00:02Z date_published: 2025-08-06T00:00:00Z date_updated: 2026-07-16T08:54:37Z day: '06' ddc: - '500' department: - _id: TiBr doi: 10.4171/jems/1697 external_id: arxiv: - '2307.05712' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.4171/JEMS/1697 month: '08' oa: 1 oa_version: Published Version project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Journal of the European Mathematical Society publication_identifier: eissn: - 1435-9863 issn: - 1435-9855 publication_status: epub_ahead publisher: EMS Press quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Quartic polynomials in two variables do not represent all non-negative integers type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: gold PlanS_conform: '1' _id: '21343' abstract: - lang: eng 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: 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.' acknowledgement: While working on this paper, the first author was supported by a FWF grant (DOI 10.55776/P36278). article_processing_charge: Yes article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Yik Tung full_name: Chan, Yik Tung id: c4c0afc8-9262-11ed-9231-d8b0bc743af1 last_name: Chan orcid: 0000-0001-8467-4106 citation: ama: Browning TD, Chan S. Solubility of a resultant equation and applications. Journal de l’ecole polytechnique mathematiques. 2025;12:1677-1691. doi:10.5802/jep.320 apa: Browning, T. D., & Chan, S. (2025). Solubility of a resultant equation and applications. Journal de l’ecole Polytechnique Mathematiques. Ecole polytechnique. https://doi.org/10.5802/jep.320 chicago: Browning, Timothy D, and Stephanie Chan. “Solubility of a Resultant Equation and Applications.” Journal de l’ecole Polytechnique Mathematiques. Ecole polytechnique, 2025. https://doi.org/10.5802/jep.320. ieee: T. D. Browning and S. Chan, “Solubility of a resultant equation and applications,” Journal de l’ecole polytechnique mathematiques, vol. 12. Ecole polytechnique, pp. 1677–1691, 2025. ista: Browning TD, Chan S. 2025. Solubility of a resultant equation and applications. Journal de l’ecole polytechnique mathematiques. 12, 1677–1691. mla: Browning, Timothy D., and Stephanie Chan. “Solubility of a Resultant Equation and Applications.” Journal de l’ecole Polytechnique Mathematiques, vol. 12, Ecole polytechnique, 2025, pp. 1677–91, doi:10.5802/jep.320. short: T.D. Browning, S. Chan, Journal de l’ecole Polytechnique Mathematiques 12 (2025) 1677–1691. corr_author: '1' das_tickbox: '0' date_created: 2026-02-22T23:01:36Z date_published: 2025-10-21T00:00:00Z date_updated: 2026-07-16T09:02:52Z day: '21' ddc: - '510' department: - _id: TiBr doi: 10.5802/jep.320 external_id: arxiv: - '2411.09264' file: - access_level: open_access checksum: 828577ea48ac6109d3e9dd1aeddd45c4 content_type: application/pdf creator: dernst date_created: 2026-02-24T07:56:34Z date_updated: 2026-02-24T07:56:34Z file_id: '21356' file_name: 2025_JEP_Browning.pdf file_size: 1003689 relation: main_file success: 1 file_date_updated: 2026-02-24T07:56:34Z has_accepted_license: '1' intvolume: ' 12' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1677-1691 project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Journal de l'ecole polytechnique mathematiques publication_identifier: eissn: - 2270-518X issn: - 2429-7100 publication_status: published publisher: Ecole polytechnique quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Solubility of a resultant equation and applications tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 12 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '18705' 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]. 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." article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas - first_name: Leonhard full_name: Hochfilzer, Leonhard last_name: Hochfilzer citation: ama: Glas J, Hochfilzer L. On a question of Davenport and diagonal cubic forms over Fq(t). Mathematische Annalen. 2025;391:5485-5533. doi:10.1007/s00208-024-03035-z apa: Glas, J., & Hochfilzer, L. (2025). On a question of Davenport and diagonal cubic forms over Fq(t). Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-024-03035-z chicago: Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” Mathematische Annalen. Springer Nature, 2025. https://doi.org/10.1007/s00208-024-03035-z. ieee: J. Glas and L. Hochfilzer, “On a question of Davenport and diagonal cubic forms over Fq(t),” Mathematische Annalen, vol. 391. Springer Nature, pp. 5485–5533, 2025. ista: Glas J, Hochfilzer L. 2025. On a question of Davenport and diagonal cubic forms over Fq(t). Mathematische Annalen. 391, 5485–5533. mla: Glas, Jakob, and Leonhard Hochfilzer. “On a Question of Davenport and Diagonal Cubic Forms over Fq(T).” Mathematische Annalen, vol. 391, Springer Nature, 2025, pp. 5485–533, doi:10.1007/s00208-024-03035-z. short: J. Glas, L. Hochfilzer, Mathematische Annalen 391 (2025) 5485–5533. corr_author: '1' das_tickbox: '1' dataavailabilitystatement: "Data sharing is not applicable to this article as no datasets were generated or analysed\r\nduring the current study." date_created: 2024-12-22T23:01:48Z date_published: 2025-04-01T00:00:00Z date_updated: 2026-07-16T09:10:29Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1007/s00208-024-03035-z external_id: arxiv: - '2208.05422' isi: - '001376740400001' file: - access_level: open_access checksum: dcf57a8b01332c36e0cf2b0d1aeecb36 content_type: application/pdf creator: dernst date_created: 2025-04-16T09:38:55Z date_updated: 2025-04-16T09:38:55Z file_id: '19579' file_name: 2025_MathAnnalen_Glas.pdf file_size: 650021 relation: main_file success: 1 file_date_updated: 2025-04-16T09:38:55Z has_accepted_license: '1' intvolume: ' 391' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 5485-5533 publication: Mathematische Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '18293' relation: earlier_version status: public researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: On a question of Davenport and diagonal cubic forms over Fq(t) tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 391 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '18822' abstract: - lang: eng 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. 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. article_number: e70008 article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 citation: ama: Wang V. Diagonal cubic forms and the large sieve. Mathematika. 2025;71(1). doi:10.1112/mtk.70008 apa: Wang, V. (2025). Diagonal cubic forms and the large sieve. Mathematika. London Mathematical Society. https://doi.org/10.1112/mtk.70008 chicago: Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” Mathematika. London Mathematical Society, 2025. https://doi.org/10.1112/mtk.70008. ieee: V. Wang, “Diagonal cubic forms and the large sieve,” Mathematika, vol. 71, no. 1. London Mathematical Society, 2025. ista: Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1), e70008. mla: Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” Mathematika, vol. 71, no. 1, e70008, London Mathematical Society, 2025, doi:10.1112/mtk.70008. short: V. Wang, Mathematika 71 (2025). corr_author: '1' das_tickbox: '0' date_created: 2025-01-12T23:04:01Z date_published: 2025-01-02T00:00:00Z date_updated: 2026-07-16T09:14:24Z day: '02' ddc: - '510' department: - _id: TiBr doi: 10.1112/mtk.70008 ec_funded: 1 external_id: isi: - '001388255500001' file: - access_level: open_access checksum: 700a8596b4bffce2320d074120962c22 content_type: application/pdf creator: dernst date_created: 2025-01-14T06:52:09Z date_updated: 2025-01-14T06:52:09Z file_id: '18845' file_name: 2025_Mathematika_Wang.pdf file_size: 309893 relation: main_file success: 1 file_date_updated: 2025-01-14T06:52:09Z has_accepted_license: '1' intvolume: ' 71' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Mathematika publication_identifier: eissn: - 2041-7942 issn: - 0025-5793 publication_status: published publisher: London Mathematical Society quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Diagonal cubic forms and the large sieve tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 71 year: '2025' ... --- OA_place: repository OA_type: green _id: '21768' abstract: - lang: eng 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 HFActa Arithmetica. 2025;221(2):141-151. doi:10.4064/aa241029-19-8 apa: Yamagishi, S. (2025). Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. Instytut Matematyczny. https://doi.org/10.4064/aa241029-19-8 chicago: Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” Acta Arithmetica. Instytut Matematyczny, 2025. https://doi.org/10.4064/aa241029-19-8. ieee: S. Yamagishi, “Birch’s theorem on forms in many variables with a Hessian condition,” Acta Arithmetica, vol. 221, no. 2. Instytut Matematyczny, pp. 141–151, 2025. ista: Yamagishi S. 2025. Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. 221(2), 141–151. mla: Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” Acta Arithmetica, vol. 221, no. 2, Instytut Matematyczny, 2025, pp. 141–51, doi:10.4064/aa241029-19-8. short: S. Yamagishi, Acta Arithmetica 221 (2025) 141–151. corr_author: '1' das_tickbox: '0' date_created: 2026-04-26T22:01:48Z date_published: 2025-10-28T00:00:00Z date_updated: 2026-07-16T09:04:43Z day: '28' department: - _id: TiBr doi: 10.4064/aa241029-19-8 external_id: arxiv: - '2304.02620' intvolume: ' 221' issue: '2' keyword: - Diophantine equations - homogeneous forms language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2304.02620 month: '10' oa: 1 oa_version: Preprint page: 141-151 project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Acta Arithmetica publication_identifier: eissn: - 1730-6264 issn: - 0065-1036 publication_status: published publisher: Instytut Matematyczny quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Birch’s theorem on forms in many variables with a Hessian condition type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 221 year: '2025' ... --- DOAJ_listed: '1' OA_place: publisher OA_type: diamond _id: '21266' 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." 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). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Yik Tung full_name: Chan, Yik Tung id: c4c0afc8-9262-11ed-9231-d8b0bc743af1 last_name: Chan orcid: 0000-0001-8467-4106 citation: ama: Browning TD, Chan S. Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society. 2025. doi:10.4171/jems/1704 apa: Browning, T. D., & Chan, S. (2025). Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society. EMS Press. https://doi.org/10.4171/jems/1704 chicago: Browning, Timothy D, and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” Journal of the European Mathematical Society. EMS Press, 2025. https://doi.org/10.4171/jems/1704. ieee: T. D. Browning and S. Chan, “Almost all quadratic twists of an elliptic curve have no integral points,” Journal of the European Mathematical Society. EMS 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. mla: Browning, Timothy D., and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” Journal of the European Mathematical Society, EMS Press, 2025, doi:10.4171/jems/1704. short: T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025). corr_author: '1' das_tickbox: '0' date_created: 2026-02-17T07:46:26Z date_published: 2025-09-17T00:00:00Z date_updated: 2026-07-16T09:00:02Z day: '17' ddc: - '510' department: - _id: TiBr doi: 10.4171/jems/1704 external_id: arxiv: - '2401.04375' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.4171/JEMS/1704 month: '09' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Journal of the European Mathematical Society publication_identifier: eissn: - 1435-9863 issn: - 1435-9855 publication_status: epub_ahead publisher: EMS Press quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Almost all quadratic twists of an elliptic curve have no integral points type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- OA_place: repository OA_type: green _id: '21265' 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. 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. article_number: rnaf279 article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 - first_name: Max Wenqiang full_name: Xu, Max Wenqiang last_name: Xu citation: ama: Wang V, Xu MW. Harper’s beyond square-root conjecture. International Mathematics Research Notices. 2025;2025(18). doi:10.1093/imrn/rnaf279 apa: Wang, V., & Xu, M. W. (2025). Harper’s beyond square-root conjecture. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaf279 chicago: Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” International Mathematics Research Notices. Oxford University Press, 2025. https://doi.org/10.1093/imrn/rnaf279. ieee: V. Wang and M. W. Xu, “Harper’s beyond square-root conjecture,” International Mathematics Research Notices, 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. mla: Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” International Mathematics Research Notices, vol. 2025, no. 18, rnaf279, Oxford University Press, 2025, doi:10.1093/imrn/rnaf279. short: V. Wang, M.W. Xu, International Mathematics Research Notices 2025 (2025). das_tickbox: '0' date_created: 2026-02-17T07:45:45Z date_published: 2025-09-01T00:00:00Z date_updated: 2026-07-16T08:57:40Z day: '01' department: - _id: TiBr doi: 10.1093/imrn/rnaf279 ec_funded: 1 external_id: arxiv: - '2405.04094' intvolume: ' 2025' issue: '18' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2405.04094 month: '09' oa: 1 oa_version: Preprint project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Harper’s beyond square-root conjecture type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 2025 year: '2025' ... --- OA_place: publisher OA_type: diamond PlanS_conform: '1' _id: '19054' 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." 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. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Loïs full_name: Faisant, Loïs id: 26ca6926-5797-11ee-9232-f8b51bd19631 last_name: Faisant citation: ama: Faisant L. Motivic distribution of rational curves and twisted products of toric varieties. Algebra & Number Theory. 2025;19:883-965. doi:10.2140/ant.2025.19.883 apa: Faisant, L. (2025). Motivic distribution of rational curves and twisted products of toric varieties. Algebra & Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2025.19.883 chicago: Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” Algebra & Number Theory. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/ant.2025.19.883. ieee: L. Faisant, “Motivic distribution of rational curves and twisted products of toric varieties,” Algebra & Number Theory, vol. 19. Mathematical Sciences Publishers, pp. 883–965, 2025. ista: Faisant L. 2025. Motivic distribution of rational curves and twisted products of toric varieties. Algebra & Number Theory. 19, 883–965. mla: Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” Algebra & Number Theory, vol. 19, Mathematical Sciences Publishers, 2025, pp. 883–965, doi:10.2140/ant.2025.19.883. short: L. Faisant, Algebra & Number Theory 19 (2025) 883–965. corr_author: '1' das_tickbox: '0' date_created: 2025-02-18T13:33:14Z date_published: 2025-04-22T00:00:00Z date_updated: 2026-07-16T09:23:01Z day: '22' ddc: - '510' department: - _id: TiBr doi: 10.2140/ant.2025.19.883 ec_funded: 1 external_id: arxiv: - '2302.07339' file: - access_level: open_access checksum: 56299f55682528a7cd0136497ce8b383 content_type: application/pdf creator: dernst date_created: 2026-02-17T13:17:00Z date_updated: 2026-02-17T13:17:00Z file_id: '21307' file_name: 2025_AlgebraNumberTheory_Faisant.pdf file_size: 2034433 relation: main_file success: 1 file_date_updated: 2026-02-17T13:17:00Z has_accepted_license: '1' intvolume: ' 19' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 883-965 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Algebra & Number Theory publication_identifier: eissn: - 1944-7833 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' researchdata_availability: no status: public supplementarymaterial: no title: Motivic distribution of rational curves and twisted products of toric varieties tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 19 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '19363' abstract: - lang: eng 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. article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: Yik Tung full_name: Chan, Yik Tung id: c4c0afc8-9262-11ed-9231-d8b0bc743af1 last_name: Chan orcid: 0000-0001-8467-4106 - first_name: Peter full_name: Koymans, Peter last_name: Koymans - first_name: Carlo full_name: Pagano, Carlo last_name: Pagano - first_name: Efthymios full_name: Sofos, Efthymios last_name: Sofos citation: ama: Chan S, Koymans P, Pagano C, Sofos E. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 2025;273:1-36. doi:10.1016/j.jnt.2025.01.005 apa: Chan, S., Koymans, P., Pagano, C., & Sofos, E. (2025). Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2025.01.005 chicago: Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “Averages of Multiplicative Functions along Equidistributed Sequences.” Journal of Number Theory. Elsevier, 2025. https://doi.org/10.1016/j.jnt.2025.01.005. ieee: S. Chan, P. Koymans, C. Pagano, and E. Sofos, “Averages of multiplicative functions along equidistributed sequences,” Journal of Number Theory, vol. 273. Elsevier, pp. 1–36, 2025. ista: Chan S, Koymans P, Pagano C, Sofos E. 2025. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 273, 1–36. mla: Chan, Stephanie, et al. “Averages of Multiplicative Functions along Equidistributed Sequences.” Journal of Number Theory, vol. 273, Elsevier, 2025, pp. 1–36, doi:10.1016/j.jnt.2025.01.005. short: S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025) 1–36. corr_author: '1' das_tickbox: '1' dataavailabilitystatement: No data was used for the research described in the article. date_created: 2025-03-09T23:01:26Z date_published: 2025-08-01T00:00:00Z date_updated: 2026-07-16T09:26:47Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1016/j.jnt.2025.01.005 external_id: isi: - '001444208500001' file: - access_level: open_access checksum: 752c407eb186d391380b10a7505f66cf content_type: application/pdf creator: dernst date_created: 2025-12-30T08:05:42Z date_updated: 2025-12-30T08:05:42Z file_id: '20889' file_name: 2025_JourNumberTheory_Chan.pdf file_size: 685204 relation: main_file success: 1 file_date_updated: 2025-12-30T08:05:42Z has_accepted_license: '1' intvolume: ' 273' isi: 1 language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 1-36 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Averages of multiplicative functions along equidistributed sequences tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 273 year: '2025' ... --- OA_place: repository OA_type: green _id: '19055' abstract: - lang: eng 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." 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" article_number: '2502.11704' article_processing_charge: No arxiv: 1 author: - first_name: Loïs full_name: Faisant, Loïs id: 26ca6926-5797-11ee-9232-f8b51bd19631 last_name: Faisant citation: ama: Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv. doi:10.48550/ARXIV.2502.11704 apa: Faisant, L. (n.d.). Motivic counting of rational curves with tangency conditions via universal torsors. arXiv. https://doi.org/10.48550/ARXIV.2502.11704 chicago: Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2502.11704. ieee: L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” arXiv. . ista: Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704. mla: Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” ArXiv, 2502.11704, doi:10.48550/ARXIV.2502.11704. short: L. Faisant, ArXiv (n.d.). corr_author: '1' das_tickbox: '0' date_created: 2025-02-18T13:34:07Z date_published: 2025-02-17T00:00:00Z date_updated: 2026-07-16T09:24:48Z day: '17' department: - _id: TiBr doi: 10.48550/ARXIV.2502.11704 ec_funded: 1 external_id: arxiv: - '2502.11704' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2502.11704 month: '02' oa: 1 oa_version: Preprint project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: arXiv publication_status: submitted researchdata_availability: no status: public supplementarymaterial: no title: Motivic counting of rational curves with tangency conditions via universal torsors type: preprint user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '19776' abstract: - lang: eng text: We use the circle method to prove that a density 1 of elements in Fq[t] are representable as a sum of three cubes of essentially minimal degree from Fq[t], assuming the Ratios Conjecture and that char(Fq)>3. Roughly speaking, to do so, we upgrade an order of magnitude result to a full asymptotic formula that was conjectured by Hooley in the number field setting. 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). article_number: '65' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Timothy D full_name: Browning, Timothy D id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 citation: ama: Browning TD, Glas J, Wang V. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 2025;310(4). doi:10.1007/s00209-025-03765-z apa: Browning, T. D., Glas, J., & Wang, V. (2025). Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-025-03765-z chicago: Browning, Timothy D, Jakob Glas, and Victor Wang. “Optimal Sums of Three Cubes in Fq[T].” Mathematische Zeitschrift. Springer Nature, 2025. https://doi.org/10.1007/s00209-025-03765-z. ieee: T. D. Browning, J. Glas, and V. Wang, “Optimal sums of three cubes in Fq[t],” Mathematische Zeitschrift, vol. 310, no. 4. Springer Nature, 2025. ista: Browning TD, Glas J, Wang V. 2025. Optimal sums of three cubes in Fq[t]. Mathematische Zeitschrift. 310(4), 65. mla: Browning, Timothy D., et al. “Optimal Sums of Three Cubes in Fq[T].” Mathematische Zeitschrift, vol. 310, no. 4, 65, Springer Nature, 2025, doi:10.1007/s00209-025-03765-z. short: T.D. Browning, J. Glas, V. Wang, Mathematische Zeitschrift 310 (2025). corr_author: '1' das_tickbox: '0' date_created: 2025-06-03T07:30:21Z date_published: 2025-05-23T00:00:00Z date_updated: 2026-07-16T10:50:51Z day: '23' ddc: - '510' department: - _id: TiBr doi: 10.1007/s00209-025-03765-z ec_funded: 1 external_id: arxiv: - '2408.03668 ' isi: - '001494367000001' file: - access_level: open_access checksum: 6f71e25740c28257bf89b8bf116c2b4d content_type: application/pdf creator: dernst date_created: 2025-06-03T08:28:14Z date_updated: 2025-06-03T08:28:14Z file_id: '19782' file_name: 2025_MathZeitschrift_Browning.pdf file_size: 461622 relation: main_file success: 1 file_date_updated: 2025-06-03T08:28:14Z has_accepted_license: '1' intvolume: ' 310' isi: 1 issue: '4' language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Mathematische Zeitschrift publication_identifier: eissn: - 1432-1823 issn: - 0025-5874 publication_status: published publisher: Springer Nature quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Optimal sums of three cubes in Fq[t] tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 310 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '19727' abstract: - lang: eng text: By studying some Clausen-like multiple Dirichlet series, we complete the proof of Manin's conjecture for sufficiently split smooth equivariant compactifications of the translation-dilation group over the rationals. Secondary terms remain elusive in general. acknowledgement: I thank Yuri Tschinkel for introducing me to the beautiful paper [53] and associated open questions, and thank him as well as Ramin Takloo-Bighash and Sho Tanimoto for their encouragement and comments. Also, I thank Tim Browning and Dan Loughran for comments and suggestions concerning Manin–Peyre, homogeneous spaces, and splitness. Thanks also to Anshul Adve, Peter Sarnak, Philip Tosteson, Katy Woo, and Nina Zubrilina for some interesting discussions. I thank the Browning Group and Andy O'Desky for many conversations. This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. Finally, I thank the editors and referees for their detailed input, which substantially improved the paper. article_number: '110341' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Victor full_name: Wang, Victor id: 76096395-aea4-11ed-a680-ab8ebbd3f1b9 last_name: Wang orcid: 0000-0002-0704-7026 citation: ama: Wang V. Asymptotic growth of translation-dilation orbits. Advances in Mathematics. 2025;475. doi:10.1016/j.aim.2025.110341 apa: Wang, V. (2025). Asymptotic growth of translation-dilation orbits. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2025.110341 chicago: Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” Advances in Mathematics. Elsevier, 2025. https://doi.org/10.1016/j.aim.2025.110341. ieee: V. Wang, “Asymptotic growth of translation-dilation orbits,” Advances in Mathematics, vol. 475. Elsevier, 2025. ista: Wang V. 2025. Asymptotic growth of translation-dilation orbits. Advances in Mathematics. 475, 110341. mla: Wang, Victor. “Asymptotic Growth of Translation-Dilation Orbits.” Advances in Mathematics, vol. 475, 110341, Elsevier, 2025, doi:10.1016/j.aim.2025.110341. short: V. Wang, Advances in Mathematics 475 (2025). corr_author: '1' das_tickbox: '0' date_created: 2025-05-25T22:16:41Z date_published: 2025-07-01T00:00:00Z date_updated: 2026-07-16T10:45:31Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1016/j.aim.2025.110341 ec_funded: 1 external_id: arxiv: - '2309.07626' isi: - '001495142300002' file: - access_level: open_access checksum: 01f2589b678ba840d6a4066c1d8d7642 content_type: application/pdf creator: dernst date_created: 2025-12-30T08:30:17Z date_updated: 2025-12-30T08:30:17Z file_id: '20895' file_name: 2025_AdvMathematics_Wang.pdf file_size: 1592341 relation: main_file success: 1 file_date_updated: 2025-12-30T08:30:17Z has_accepted_license: '1' intvolume: ' 475' isi: 1 language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Advances in Mathematics publication_identifier: eissn: - 1090-2082 issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' researchdata_availability: no scopus_import: '1' status: public supplementarymaterial: no title: Asymptotic growth of translation-dilation orbits tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 475 year: '2025' ...