--- 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' date_created: 2025-05-25T22:16:41Z date_published: 2025-07-01T00:00:00Z date_updated: 2025-12-30T08:30:30Z 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' scopus_import: '1' status: public 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: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 475 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' date_created: 2025-06-03T07:30:21Z date_published: 2025-05-23T00:00:00Z date_updated: 2025-09-30T12:43:41Z 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' scopus_import: '1' status: public 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: '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. 2025;279:170-183. doi:10.1016/j.jnt.2025.06.001 apa: Barańczuk, S., Naskręcki, B., & Verzobio, M. (2025). 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, 2025. 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, 2025. ista: Barańczuk S, Naskręcki B, Verzobio M. 2025. 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, 2025, pp. 170–83, doi:10.1016/j.jnt.2025.06.001. short: S. Barańczuk, B. Naskręcki, M. Verzobio, Journal of Number Theory 279 (2025) 170–183. corr_author: '1' date_created: 2025-07-27T22:01:25Z date_published: 2025-07-23T00:00:00Z date_updated: 2026-06-18T18:19:48Z day: '23' ddc: - '500' department: - _id: TiBr doi: 10.1016/j.jnt.2025.06.001 external_id: arxiv: - '2309.09699' isi: - '001541172400002' intvolume: ' 279' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1016/j.jnt.2025.06.001 month: '07' oa: 1 oa_version: Published Version page: 170-183 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: epub_ahead publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 279 year: '2025' ... --- OA_place: publisher OA_type: hybrid _id: '20222' abstract: - lang: eng text: Let X be a smooth projective hypersurface defined over Q. We provide new bounds for rational points of bounded height on X. In particular, we show that if X is a smooth projective hypersurface in Pn with n 4 and degree d 50, then the set of rational points on X of height bounded by B have cardinality On,d,ε (Bn−2+ε ). If X is smooth and has degree d 6, we improve the dimension growth conjecture bound. We achieve an analogue result for affine hypersurfaces whose projective closure is smooth. acknowledgement: "While working on this paper, the author was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. The author is very grateful to Tim Browning for suggesting the problem and for many useful discussions. We thank the anonymous referees for their many helpful comments, which improved the exposition of the paper. We are also grateful to Gal Binyamini for their interest in this work and for drawing our attention to the aforementioned paper [1].\r\nWe shared an early version of this paper with Per Salberger, who mentioned that he announced a new bound for smooth threefolds in P4 during a talk in 2019 (see [7] for the abstract). This result has not been published." article_number: rnaf249 article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: ama: Verzobio M. Counting rational points on smooth hypersurfaces with high degree. International Mathematics Research Notices. 2025;2025(16). doi:10.1093/imrn/rnaf249 apa: Verzobio, M. (2025). Counting rational points on smooth hypersurfaces with high degree. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnaf249 chicago: Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High Degree.” International Mathematics Research Notices. Oxford University Press, 2025. https://doi.org/10.1093/imrn/rnaf249. ieee: M. Verzobio, “Counting rational points on smooth hypersurfaces with high degree,” International Mathematics Research Notices, vol. 2025, no. 16. Oxford University Press, 2025. ista: Verzobio M. 2025. Counting rational points on smooth hypersurfaces with high degree. International Mathematics Research Notices. 2025(16), rnaf249. mla: Verzobio, Matteo. “Counting Rational Points on Smooth Hypersurfaces with High Degree.” International Mathematics Research Notices, vol. 2025, no. 16, rnaf249, Oxford University Press, 2025, doi:10.1093/imrn/rnaf249. short: M. Verzobio, International Mathematics Research Notices 2025 (2025). corr_author: '1' date_created: 2025-08-24T22:01:31Z date_published: 2025-08-01T00:00:00Z date_updated: 2025-09-30T14:26:34Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1093/imrn/rnaf249 ec_funded: 1 external_id: arxiv: - '2503.19451' isi: - '001549126000001' file: - access_level: open_access checksum: 482ae2be98841ee446cf2bdfcd79f86f content_type: application/pdf creator: dernst date_created: 2025-09-02T07:55:05Z date_updated: 2025-09-02T07:55:05Z file_id: '20275' file_name: 2025_IMRN_Verzobio.pdf file_size: 540263 relation: main_file success: 1 file_date_updated: 2025-09-02T07:55:05Z has_accepted_license: '1' intvolume: ' 2025' isi: 1 issue: '16' language: - iso: eng month: '08' 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: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: Counting rational points on smooth hypersurfaces with high degree tmp: image: /images/cc_by_nc_nd.png legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) short: CC BY-NC-ND (4.0) type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 2025 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20249' 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. 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)." article_number: '81' 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: Florian Alexander full_name: Wilsch, Florian Alexander id: 560601DA-8D36-11E9-A136-7AC1E5697425 last_name: Wilsch orcid: 0000-0001-7302-8256 citation: ama: 'Browning TD, Wilsch FA. Integral points on cubic surfaces: heuristics and numerics. Selecta Mathematica New Series. 2025;31(4). doi:10.1007/s00029-025-01074-1' apa: 'Browning, T. D., & Wilsch, F. A. (2025). Integral points on cubic surfaces: heuristics and numerics. Selecta Mathematica New Series. Springer Nature. https://doi.org/10.1007/s00029-025-01074-1' chicago: 'Browning, Timothy D, and Florian Alexander Wilsch. “Integral Points on Cubic Surfaces: Heuristics and Numerics.” Selecta Mathematica New Series. Springer Nature, 2025. https://doi.org/10.1007/s00029-025-01074-1.' ieee: 'T. D. Browning and F. A. Wilsch, “Integral points on cubic surfaces: heuristics and numerics,” Selecta Mathematica New Series, vol. 31, no. 4. Springer Nature, 2025.' ista: 'Browning TD, Wilsch FA. 2025. Integral points on cubic surfaces: heuristics and numerics. Selecta Mathematica New Series. 31(4), 81.' mla: 'Browning, Timothy D., and Florian Alexander Wilsch. “Integral Points on Cubic Surfaces: Heuristics and Numerics.” Selecta Mathematica New Series, vol. 31, no. 4, 81, Springer Nature, 2025, doi:10.1007/s00029-025-01074-1.' short: T.D. Browning, F.A. Wilsch, Selecta Mathematica New Series 31 (2025). corr_author: '1' date_created: 2025-08-31T22:01:31Z date_published: 2025-09-01T00:00:00Z date_updated: 2025-09-30T14:29:25Z day: '01' ddc: - '500' department: - _id: TiBr doi: 10.1007/s00029-025-01074-1 external_id: arxiv: - '2407.16315' isi: - '001552779800001' file: - access_level: open_access checksum: 89352f1f7e8d2b367ae5f4e9bf9eb1f5 content_type: application/pdf creator: dernst date_created: 2025-09-03T06:44:44Z date_updated: 2025-09-03T06:44:44Z file_id: '20281' file_name: 2025_SelectaMathematica_Browning.pdf file_size: 2484757 relation: main_file success: 1 file_date_updated: 2025-09-03T06:44:44Z has_accepted_license: '1' intvolume: ' 31' isi: 1 issue: '4' language: - iso: eng month: '09' 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 - _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3 grant_number: P36278 name: Rational curves via function field analytic number theory publication: Selecta Mathematica New Series publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: 'Integral points on cubic surfaces: heuristics and numerics' 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: 31 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20367' abstract: - lang: eng 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. 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). 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: Will full_name: Sawin, Will last_name: Sawin - 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, Sawin W, Wang V. Pairs of commuting integer matrices. Mathematische Annalen. 2025;393:1863–1880. doi:10.1007/s00208-025-03285-5 apa: Browning, T. D., Sawin, W., & Wang, V. (2025). Pairs of commuting integer matrices. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-025-03285-5 chicago: Browning, Timothy D, Will Sawin, and Victor Wang. “Pairs of Commuting Integer Matrices.” Mathematische Annalen. Springer Nature, 2025. https://doi.org/10.1007/s00208-025-03285-5. ieee: T. D. Browning, W. Sawin, and V. Wang, “Pairs of commuting integer matrices,” Mathematische Annalen, vol. 393. Springer Nature, pp. 1863–1880, 2025. ista: Browning TD, Sawin W, Wang V. 2025. Pairs of commuting integer matrices. Mathematische Annalen. 393, 1863–1880. mla: Browning, Timothy D., et al. “Pairs of Commuting Integer Matrices.” Mathematische Annalen, vol. 393, Springer Nature, 2025, pp. 1863–1880, doi:10.1007/s00208-025-03285-5. short: T.D. Browning, W. Sawin, V. Wang, Mathematische Annalen 393 (2025) 1863–1880. corr_author: '1' date_created: 2025-09-21T22:01:31Z date_published: 2025-10-01T00:00:00Z date_updated: 2026-01-05T13:15:53Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1007/s00208-025-03285-5 ec_funded: 1 external_id: arxiv: - '2409.01920' isi: - '001567740200001' file: - access_level: open_access checksum: 1e94da1a67306e03c8e0086518faf4bc content_type: application/pdf creator: dernst date_created: 2026-01-05T13:15:44Z date_updated: 2026-01-05T13:15:44Z file_id: '20950' file_name: 2025_MathAnnalen_Browning.pdf file_size: 337505 relation: main_file success: 1 file_date_updated: 2026-01-05T13:15:44Z has_accepted_license: '1' intvolume: ' 393' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1863–1880 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 Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Pairs of commuting integer matrices 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: 393 year: '2025' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '20423' abstract: - lang: eng text: "For any d 2, we prove that there exists an integer n0(d) such that there exists an n × n\r\nmagic square of dth powers for all n n0(d). In particular, we establish the existence of\r\nan n × n magic square of squares for all n 4, which settles a conjecture of\r\nVárilly-Alvarado. All previous approaches had been based on constructive methods and\r\nthe existence of n × n magic squares of dth powers had only been known for sparse\r\nvalues of n. We prove our result by the Hardy-Littlewood circle method, which in this\r\nsetting essentially reduces the problem to finding a sufficient number of disjoint linearly\r\nindependent subsets of the columns of the coefficient matrix of the equations defining\r\nmagic squares. We prove an optimal (up to a constant) lower bound for this quantity." acknowledgement: "The authors are grateful to Tim Browning for his constant encouragement and enthusiasm, Jörg Brüdern for very helpful discussion regarding his paper [1] and Diyuan Wu for turning the proof of Theorem 2.4 in the original version into an algorithm and running the computation for us, for which the results are available in the appendix of the original version. They would also like to thank Christian Boyer for maintaining his website [4] which contains a comprehensive list of various magic squares discovered, Brady Haran and Tony Várilly-Alvarado for their public engagement activity of mathematics and magic squares of squares (A YouTube video “Magic Squares of Squares (are PROBABLY impossible)” of the Numberphile channel by Brady Haran, in which Tony Várilly-Alvarado appears as a guest speaker: https://www.youtube.com/watch?v=Kdsj84UdeYg.), and all the magic squares enthusiasts who have contributed to [4] which made this paper possible. Finally, the authors would like to thank the anonymous referees for their helpful comments, Daniel Flores for his work [11] which inspired them to optimise the proof of Theorem 2.4 and Trevor Wooley for very helpful discussion regarding recent developments in Waring’s problem and his comments on the original version of this paper.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). NR was supported by FWF project ESP 441-NBL while SY by a FWF grant (DOI 10.55776/P32428)." article_number: '91' article_processing_charge: Yes (via OA deal) 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. On the existence of magic squares of powers. Research in Number Theory. 2025;11(4). doi:10.1007/s40993-025-00671-5 apa: Rome, N., & Yamagishi, S. (2025). On the existence of magic squares of powers. Research in Number Theory. Springer Nature. https://doi.org/10.1007/s40993-025-00671-5 chicago: Rome, Nick, and Shuntaro Yamagishi. “On the Existence of Magic Squares of Powers.” Research in Number Theory. Springer Nature, 2025. https://doi.org/10.1007/s40993-025-00671-5. ieee: N. Rome and S. Yamagishi, “On the existence of magic squares of powers,” Research in Number Theory, vol. 11, no. 4. Springer Nature, 2025. ista: Rome N, Yamagishi S. 2025. On the existence of magic squares of powers. Research in Number Theory. 11(4), 91. mla: Rome, Nick, and Shuntaro Yamagishi. “On the Existence of Magic Squares of Powers.” Research in Number Theory, vol. 11, no. 4, 91, Springer Nature, 2025, doi:10.1007/s40993-025-00671-5. short: N. Rome, S. Yamagishi, Research in Number Theory 11 (2025). corr_author: '1' date_created: 2025-10-05T22:01:34Z date_published: 2025-09-23T00:00:00Z date_updated: 2025-10-13T12:30:40Z day: '23' ddc: - '510' department: - _id: TiBr doi: 10.1007/s40993-025-00671-5 external_id: arxiv: - '2406.09364' file: - access_level: open_access checksum: d41fbdc0cfc1fbceb519eb49b20a3ec2 content_type: application/pdf creator: dernst date_created: 2025-10-13T11:28:49Z date_updated: 2025-10-13T11:28:49Z file_id: '20463' file_name: 2025_ResearchNumberTheory_Rome.pdf file_size: 428531 relation: main_file success: 1 file_date_updated: 2025-10-13T11:28:49Z has_accepted_license: '1' intvolume: ' 11' issue: '4' language: - iso: eng month: '09' 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: Research in Number Theory publication_identifier: eissn: - 2363-9555 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the existence of magic squares of powers 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: 11 year: '2025' ... --- OA_type: closed access _id: '20603' abstract: - lang: eng text: "We study the growth of sumsets A+B⊂S⊂G, where S does not contain an arithmetic progression of length 2k+1, and where G is a commutative group, in which every nonzero element has an order of at least 2k+1. More specifically, we show the following: if A,B⊂G are sets such that A+B does not contain an arithmetic progression of length 2k+1, then\r\n|A+B|≥|A|2k−13k−2|B|k3k−2.\r\nAs an application we derive upper bounds on the cardinality of the summands in sumsets A+B+C contained in the set of t-th powers, where t≥2 is an integer. In particular, we show that min(|A|,|B|,|C|)≪(logN)4/5 for t=2, and min(|A|,|B|,|C|)≪t(logN)1/2 for t≥3." acknowledgement: "The authors would like to thank the referee and Ilya Shkredov for comments on the manuscript.\r\nC. E. is supported by a joint FWF-ANR project ArithRand, grant numbers FWF I 4945-N and ANR-20-CE91-0006.\r\n" article_processing_charge: No article_type: original author: - first_name: Christian full_name: Elsholtz, Christian last_name: Elsholtz - first_name: Imre Z. full_name: Ruzsa, Imre Z. last_name: Ruzsa - first_name: Lena full_name: Wurzinger, Lena id: 50c57d72-32a8-11ee-aeea-d652094d2ccd last_name: Wurzinger orcid: 0009-0004-5360-0074 citation: ama: Elsholtz C, Ruzsa IZ, Wurzinger L. Sumset growth in progression-free sets. Acta Arithmetica. 2025;220:289-303. doi:10.4064/aa250115-14-7 apa: Elsholtz, C., Ruzsa, I. Z., & Wurzinger, L. (2025). Sumset growth in progression-free sets. Acta Arithmetica. Institute of Mathematics. https://doi.org/10.4064/aa250115-14-7 chicago: Elsholtz, Christian, Imre Z. Ruzsa, and Lena Wurzinger. “Sumset Growth in Progression-Free Sets.” Acta Arithmetica. Institute of Mathematics, 2025. https://doi.org/10.4064/aa250115-14-7. ieee: C. Elsholtz, I. Z. Ruzsa, and L. Wurzinger, “Sumset growth in progression-free sets,” Acta Arithmetica, vol. 220. Institute of Mathematics, pp. 289–303, 2025. ista: Elsholtz C, Ruzsa IZ, Wurzinger L. 2025. Sumset growth in progression-free sets. Acta Arithmetica. 220, 289–303. mla: Elsholtz, Christian, et al. “Sumset Growth in Progression-Free Sets.” Acta Arithmetica, vol. 220, Institute of Mathematics, 2025, pp. 289–303, doi:10.4064/aa250115-14-7. short: C. Elsholtz, I.Z. Ruzsa, L. Wurzinger, Acta Arithmetica 220 (2025) 289–303. corr_author: '1' date_created: 2025-11-04T14:33:16Z date_published: 2025-09-12T00:00:00Z date_updated: 2025-12-01T15:18:09Z day: '12' department: - _id: TiBr doi: 10.4064/aa250115-14-7 external_id: isi: - '001570716800001' intvolume: ' 220' isi: 1 language: - iso: eng month: '09' oa_version: None page: 289-303 publication: Acta Arithmetica publication_identifier: eissn: - 1730-6264 issn: - 0065-1036 publication_status: published publisher: Institute of Mathematics quality_controlled: '1' scopus_import: '1' status: public title: Sumset growth in progression-free sets type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 220 year: '2025' ... --- _id: '12312' abstract: - lang: eng text: "Let $\\ell$ be a prime number. We classify the subgroups $G$ of $\\operatorname{Sp}_4(\\mathbb{F}_\\ell)$ and $\\operatorname{GSp}_4(\\mathbb{F}_\\ell)$ that act irreducibly on $\\mathbb{F}_\\ell^4$, but such that every element of $G$ fixes an $\\mathbb{F}_\\ell$-vector subspace of dimension 1. We use this classification to prove that the local-global principle for isogenies of degree $\\ell$ between abelian surfaces over number fields holds in many cases -- in particular, whenever the abelian surface has non-trivial endomorphisms and $\\ell$ is large enough with respect to the field of definition. Finally, we prove that there exist arbitrarily large primes $\\ell$ for which some abelian surface\r\n$A/\\mathbb{Q}$ fails the local-global principle for isogenies of degree $\\ell$." acknowledgement: "It is a pleasure to thank Samuele Anni for his interest in this project and for several discussions on the topic of this paper, which led in particular to Remark 6.30 and to a better understanding of the difficulties with [6]. We also thank John Cullinan for correspondence about [6] and Barinder Banwait for his many insightful comments on the first version of this paper. Finally, we thank the referee for their thorough reading of the manuscript.\r\nOpen access funding provided by Università di Pisa within the CRUI-CARE Agreement. The authors have been partially supported by MIUR (Italy) through PRIN 2017 “Geometric, algebraic and analytic methods in arithmetic\" and PRIN 2022 “Semiabelian varieties, Galois representations and related Diophantine problems\", and by the University of Pisa through PRA 2018-19 and 2022 “Spazi di moduli, rappresentazioni e strutture combinatorie\". The first author is a member of the INdAM group GNSAGA." article_number: '18' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Davide full_name: Lombardo, Davide last_name: Lombardo - first_name: Matteo full_name: Verzobio, Matteo id: 7aa8f170-131e-11ed-88e1-a9efd01027cb last_name: Verzobio orcid: 0000-0002-0854-0306 citation: ama: Lombardo D, Verzobio M. On the local-global principle for isogenies of abelian surfaces. Selecta Mathematica. 2024;30(2). doi:10.1007/s00029-023-00908-0 apa: Lombardo, D., & Verzobio, M. (2024). On the local-global principle for isogenies of abelian surfaces. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-023-00908-0 chicago: Lombardo, Davide, and Matteo Verzobio. “On the Local-Global Principle for Isogenies of Abelian Surfaces.” Selecta Mathematica. Springer Nature, 2024. https://doi.org/10.1007/s00029-023-00908-0. ieee: D. Lombardo and M. Verzobio, “On the local-global principle for isogenies of abelian surfaces,” Selecta Mathematica, vol. 30, no. 2. Springer Nature, 2024. ista: Lombardo D, Verzobio M. 2024. On the local-global principle for isogenies of abelian surfaces. Selecta Mathematica. 30(2), 18. mla: Lombardo, Davide, and Matteo Verzobio. “On the Local-Global Principle for Isogenies of Abelian Surfaces.” Selecta Mathematica, vol. 30, no. 2, 18, Springer Nature, 2024, doi:10.1007/s00029-023-00908-0. short: D. Lombardo, M. Verzobio, Selecta Mathematica 30 (2024). corr_author: '1' date_created: 2023-01-16T11:45:53Z date_published: 2024-01-26T00:00:00Z date_updated: 2025-08-05T13:26:34Z day: '26' ddc: - '510' department: - _id: TiBr doi: 10.1007/s00029-023-00908-0 external_id: arxiv: - '2206.15240' isi: - '001148959100001' file: - access_level: open_access checksum: ae75441420aabd80c5828bce38272ba1 content_type: application/pdf creator: dernst date_created: 2024-07-22T09:33:58Z date_updated: 2024-07-22T09:33:58Z file_id: '17298' file_name: 2024_SelectaMath_Lombardo.pdf file_size: 1301415 relation: main_file success: 1 file_date_updated: 2024-07-22T09:33:58Z has_accepted_license: '1' intvolume: ' 30' isi: 1 issue: '2' language: - iso: eng month: '01' oa: 1 oa_version: Published Version publication: Selecta Mathematica publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the local-global principle for isogenies of abelian surfaces 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: 30 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15312' 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. 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: Igor E. full_name: Shparlinski, Igor E. last_name: Shparlinski citation: ama: Browning TD, Shparlinski IE. Square-free values of random polynomials. Journal of Number Theory. 2024;261:220-240. doi:10.1016/j.jnt.2024.02.013 apa: Browning, T. D., & Shparlinski, I. E. (2024). Square-free values of random polynomials. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2024.02.013 chicago: Browning, Timothy D, and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” Journal of Number Theory. Elsevier, 2024. https://doi.org/10.1016/j.jnt.2024.02.013. ieee: T. D. Browning and I. E. Shparlinski, “Square-free values of random polynomials,” Journal of Number Theory, vol. 261. Elsevier, pp. 220–240, 2024. ista: Browning TD, Shparlinski IE. 2024. Square-free values of random polynomials. Journal of Number Theory. 261, 220–240. mla: Browning, Timothy D., and Igor E. Shparlinski. “Square-Free Values of Random Polynomials.” Journal of Number Theory, vol. 261, Elsevier, 2024, pp. 220–40, doi:10.1016/j.jnt.2024.02.013. short: T.D. Browning, I.E. Shparlinski, Journal of Number Theory 261 (2024) 220–240. corr_author: '1' date_created: 2024-04-14T22:01:00Z date_published: 2024-08-01T00:00:00Z date_updated: 2025-09-04T13:47:43Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1016/j.jnt.2024.02.013 external_id: arxiv: - '2305.15493' isi: - '001220725000001' file: - access_level: open_access checksum: 614032802febde0aa8e904e9a8ef99ab content_type: application/pdf creator: dernst date_created: 2025-01-09T09:00:02Z date_updated: 2025-01-09T09:00:02Z file_id: '18794' file_name: 2024_JourNumberTheory_Browning.pdf file_size: 394850 relation: main_file success: 1 file_date_updated: 2025-01-09T09:00:02Z has_accepted_license: '1' intvolume: ' 261' isi: 1 language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 220-240 publication: Journal of Number Theory publication_identifier: issn: - 0022-314X publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Square-free values of random 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: 261 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15337' abstract: - lang: eng 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). 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. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Dante full_name: Bonolis, Dante id: 6A459894-5FDD-11E9-AF35-BB24E6697425 last_name: Bonolis - 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: Zhizhong full_name: Huang, Zhizhong id: 21f1b52f-2fd1-11eb-a347-a4cdb9b18a51 last_name: Huang citation: ama: Bonolis D, Browning TD, Huang Z. Density of rational points on some quadric bundle threefolds. Mathematische Annalen. 2024;390:4123-4207. doi:10.1007/s00208-024-02854-4 apa: Bonolis, D., Browning, T. D., & Huang, Z. (2024). Density of rational points on some quadric bundle threefolds. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-024-02854-4 chicago: Bonolis, Dante, Timothy D Browning, and Zhizhong Huang. “Density of Rational Points on Some Quadric Bundle Threefolds.” Mathematische Annalen. Springer Nature, 2024. https://doi.org/10.1007/s00208-024-02854-4. ieee: D. Bonolis, T. D. Browning, and Z. Huang, “Density of rational points on some quadric bundle threefolds,” Mathematische Annalen, vol. 390. Springer Nature, pp. 4123–4207, 2024. ista: Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some quadric bundle threefolds. Mathematische Annalen. 390, 4123–4207. mla: Bonolis, Dante, et al. “Density of Rational Points on Some Quadric Bundle Threefolds.” Mathematische Annalen, vol. 390, Springer Nature, 2024, pp. 4123–207, doi:10.1007/s00208-024-02854-4. short: D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207. corr_author: '1' date_created: 2024-04-21T22:00:53Z date_published: 2024-11-01T00:00:00Z date_updated: 2025-09-04T13:41:19Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1007/s00208-024-02854-4 external_id: arxiv: - '2204.09322' isi: - '001204670500001' file: - access_level: open_access checksum: 5dd51531deb1e4760c38c3c0c7d5aedc content_type: application/pdf creator: dernst date_created: 2025-01-09T09:08:14Z date_updated: 2025-01-09T09:08:14Z file_id: '18796' file_name: 2024_MathAnnalen_Bonolis.pdf file_size: 1019116 relation: main_file success: 1 file_date_updated: 2025-01-09T09:08:14Z has_accepted_license: '1' intvolume: ' 390' isi: 1 language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 4123-4207 project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Mathematische Annalen publication_identifier: eissn: - 1432-1807 issn: - 0025-5831 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Density of rational points on some quadric bundle threefolds 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: 390 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '15338' 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. 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. 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: Lillian B. full_name: Pierce, Lillian B. last_name: Pierce - first_name: Damaris full_name: Schindler, Damaris last_name: Schindler citation: ama: Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. 2024;23(6):2859-2912. doi:10.1017/S1474748024000161 apa: Browning, T. D., Pierce, L. B., & Schindler, D. (2024). Generalised quadratic forms over totally real number fields. Journal of the Institute of Mathematics of Jussieu. Cambridge University Press. https://doi.org/10.1017/S1474748024000161 chicago: Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised Quadratic Forms over Totally Real Number Fields.” Journal of the Institute of Mathematics of Jussieu. Cambridge University Press, 2024. https://doi.org/10.1017/S1474748024000161. ieee: T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms over totally real number fields,” Journal of the Institute of Mathematics of Jussieu, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024. 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. mla: Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real Number Fields.” Journal of the Institute of Mathematics of Jussieu, vol. 23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:10.1017/S1474748024000161. short: T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics of Jussieu 23 (2024) 2859–2912. corr_author: '1' date_created: 2024-04-21T22:00:53Z date_published: 2024-11-01T00:00:00Z date_updated: 2025-09-04T13:44:16Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1017/S1474748024000161 external_id: arxiv: - '2212.11038' isi: - '001200337400001' file: - access_level: open_access checksum: b300541d581a71d92314df5ae8c4cc09 content_type: application/pdf creator: dernst date_created: 2025-01-09T08:56:33Z date_updated: 2025-01-09T08:56:33Z file_id: '18793' file_name: 2024_JournInstMathJussieu_Browning.pdf file_size: 690974 relation: main_file success: 1 file_date_updated: 2025-01-09T08:56:33Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '6' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 2859-2912 project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Journal of the Institute of Mathematics of Jussieu publication_identifier: eissn: - 1475-3030 issn: - 1474-7480 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Generalised quadratic forms over totally real number fields 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: 23 year: '2024' ... --- _id: '17127' abstract: - lang: eng text: "Let P(x)∈Z[x] be a polynomial with at least two distinct complex roots. We prove that the number of solutions (x1,…,xk,y1,…,yk)∈[N]2k to the equation\r\n∏1≤i≤kP(xi)=∏1≤j≤kP(yj)≠0\r\n(for any k≥1 ) is asymptotically k!Nk as N→+∞. This solves a question first proposed and studied by Najnudel. The result can also be interpreted as saying that all even moments of random partial sums 1N√∑n≤Nf(P(n)) match standard complex Gaussian moments as N→+∞\r\n , where f is the Steinhaus random multiplicative function." acknowledgement: 'We thank Oleksiy Klurman, Ilya Shkredov, and Igor Shparlinski for helpful comments on earlier versions of the paper, and thank Yotam Hendel for providing a reference for Lemma 2.1. We also thank the anonymous referee for their generous corrections and comments. The first author has received funding from the European Union''s Horizon 2020 Research and Innovation Program under the Marie Skłodowska-Curie Grant Agreement Number: 101034413. The second author is partially supported by the Cuthbert C. Hurd Graduate Fellowship in the Mathematical Sciences, Stanford.' 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. Paucity phenomena for polynomial products. Bulletin of the London Mathematical Society. 2024;56(8):2718-2726. doi:10.1112/blms.13095 apa: Wang, V., & Xu, M. W. (2024). Paucity phenomena for polynomial products. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.13095 chicago: Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.” Bulletin of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/blms.13095. ieee: V. Wang and M. W. Xu, “Paucity phenomena for polynomial products,” Bulletin of the London Mathematical Society, vol. 56, no. 8. London Mathematical Society, pp. 2718–2726, 2024. ista: Wang V, Xu MW. 2024. Paucity phenomena for polynomial products. Bulletin of the London Mathematical Society. 56(8), 2718–2726. mla: Wang, Victor, and Max Wenqiang Xu. “Paucity Phenomena for Polynomial Products.” Bulletin of the London Mathematical Society, vol. 56, no. 8, London Mathematical Society, 2024, pp. 2718–26, doi:10.1112/blms.13095. short: V. Wang, M.W. Xu, Bulletin of the London Mathematical Society 56 (2024) 2718–2726. date_created: 2024-06-09T22:01:03Z date_published: 2024-08-01T00:00:00Z date_updated: 2025-09-08T08:57:32Z day: '01' ddc: - '512' department: - _id: TiBr doi: 10.1112/blms.13095 ec_funded: 1 external_id: arxiv: - '2211.02908' isi: - '001235729900001' file: - access_level: open_access checksum: ae386a4031856efac23c7cdcb53b559b content_type: application/pdf creator: vwang date_created: 2024-08-20T08:36:32Z date_updated: 2024-08-20T08:36:32Z file_id: '17446' file_name: Paucity_phenomena_for_polynomial_products__Wang_Xu_ (7).pdf file_size: 331775 relation: main_file success: 1 file_date_updated: 2024-08-20T08:36:32Z has_accepted_license: '1' intvolume: ' 56' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2211.02908 month: '08' oa: 1 oa_version: Submitted Version page: 2718-2726 project: - _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c call_identifier: H2020 grant_number: '101034413' name: 'IST-BRIDGE: International postdoctoral program' publication: Bulletin of the London Mathematical Society publication_identifier: eissn: - 1469-2120 issn: - 0024-6093 publication_status: published publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Paucity phenomena for polynomial products type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 56 year: '2024' ... --- OA_place: publisher OA_type: hybrid PlanS_conform: '1' _id: '18930' abstract: - lang: eng text: "We study sumsets \U0001D49C + ℬ in the set of squares \U0001D4AE (and, more generally, in the set of kth powers \U0001D4AEk, where k ≥2 is an integer). It is known by a result of Gyarmati that \U0001D49C + ℬ ⊂ \U0001D4AEk ∩[1,N] implies that min(|\U0001D49C|,|ℬ|) =Ok(logN). Here, we study how the upper bound on |ℬ| decreases, when the size of |\U0001D49C| increases (or vice versa). In particular, if |\U0001D49C| ≥ Ck1m m(logN)1m , then |ℬ| = Ok(m2logN), for sufficiently large N, a positive integer m and an explicit constant C > 0. For example, with m ∼ loglogN this gives: If |\U0001D49C| ≥ CkloglogN,then |ℬ| = Ok(logN(loglogN)2)." acknowledgement: This manuscript grew out of the second author’s MSc Thesis at Graz University of Technology [34]. C. Elsholtz is supported by a joint FWF-ANR project ArithRand, grant numbers FWF I 4945-N and ANR-20-CE91-0006. Both authors would like to thank Igor Shparlinski for drawing our attention to related character sum estimates. Furthermore, we would like to thank the referee for a careful reading of the paper. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Christian full_name: Elsholtz, Christian last_name: Elsholtz - first_name: Lena full_name: Wurzinger, Lena id: 50c57d72-32a8-11ee-aeea-d652094d2ccd last_name: Wurzinger orcid: 0009-0004-5360-0074 citation: ama: Elsholtz C, Wurzinger L. Sumsets in the set of squares. The Quarterly Journal of Mathematics. 2024;75(4):1243-1254. doi:10.1093/qmath/haae044 apa: Elsholtz, C., & Wurzinger, L. (2024). Sumsets in the set of squares. The Quarterly Journal of Mathematics. Oxford University Press. https://doi.org/10.1093/qmath/haae044 chicago: Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.” The Quarterly Journal of Mathematics. Oxford University Press, 2024. https://doi.org/10.1093/qmath/haae044. ieee: C. Elsholtz and L. Wurzinger, “Sumsets in the set of squares,” The Quarterly Journal of Mathematics, vol. 75, no. 4. Oxford University Press, pp. 1243–1254, 2024. ista: Elsholtz C, Wurzinger L. 2024. Sumsets in the set of squares. The Quarterly Journal of Mathematics. 75(4), 1243–1254. mla: Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.” The Quarterly Journal of Mathematics, vol. 75, no. 4, Oxford University Press, 2024, pp. 1243–54, doi:10.1093/qmath/haae044. short: C. Elsholtz, L. Wurzinger, The Quarterly Journal of Mathematics 75 (2024) 1243–1254. corr_author: '1' date_created: 2025-01-28T06:55:31Z date_published: 2024-12-01T00:00:00Z date_updated: 2025-12-04T14:46:28Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1093/qmath/haae044 external_id: isi: - '001304396600001' file: - access_level: open_access checksum: 1a06e052761d3f1e873463d6f529dd82 content_type: application/pdf creator: dernst date_created: 2025-01-28T07:03:51Z date_updated: 2025-01-28T07:03:51Z file_id: '18931' file_name: 2024_QuarterlyJourMath_Elsholtz.pdf file_size: 424645 relation: main_file success: 1 file_date_updated: 2025-01-28T07:03:51Z has_accepted_license: '1' intvolume: ' 75' isi: 1 issue: '4' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 1243-1254 publication: The Quarterly Journal of Mathematics publication_identifier: eissn: - 1464-3847 issn: - 0033-5606 publication_status: published publisher: Oxford University Press quality_controlled: '1' scopus_import: '1' status: public title: Sumsets in the set of squares 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: 75 year: '2024' ... --- OA_place: repository _id: '19013' abstract: - lang: eng text: We study the singularities of the moduli space of degree e maps from smooth genus g curves to an arbitrary smooth hypersurface of low degree. For e large compared to g, we show that these moduli spaces have at worst terminal singularities. Our main approach is to study the jet schemes of these moduli spaces by developing a suitable form of the circle method. article_processing_charge: No arxiv: 1 author: - first_name: Jakob full_name: Glas, Jakob id: d6423cba-dc74-11ea-a0a7-ee61689ff5fb last_name: Glas - first_name: 'Matthew ' full_name: 'Hase-Liu, Matthew ' last_name: Hase-Liu citation: ama: Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. arXiv. doi:10.48550/arXiv.2412.14923 apa: Glas, J., & Hase-Liu, M. (n.d.). Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. arXiv. https://doi.org/10.48550/arXiv.2412.14923 chicago: Glas, Jakob, and Matthew Hase-Liu. “Terminal Singularities of the Moduli Space of Curves on Low Degree Hypersurfaces and the Circle Method.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2412.14923. ieee: J. Glas and M. Hase-Liu, “Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method,” arXiv. . ista: Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. arXiv, 10.48550/arXiv.2412.14923. mla: Glas, Jakob, and Matthew Hase-Liu. “Terminal Singularities of the Moduli Space of Curves on Low Degree Hypersurfaces and the Circle Method.” ArXiv, doi:10.48550/arXiv.2412.14923. short: J. Glas, M. Hase-Liu, ArXiv (n.d.). corr_author: '1' date_created: 2025-02-07T12:04:11Z date_published: 2024-12-19T00:00:00Z date_updated: 2025-04-15T08:05:40Z day: '19' department: - _id: TiBr doi: 10.48550/arXiv.2412.14923 external_id: arxiv: - '2412.14923' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2412.14923 month: '12' oa: 1 oa_version: Preprint publication: arXiv publication_status: draft related_material: record: - id: '18295' relation: earlier_version status: public status: public title: Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method 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: preprint user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '19051' abstract: - lang: eng text: This paper corrects an error in an earlier work of the author. 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 polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. 2024;2024(13):10165-10168. doi:10.1093/imrn/rnae066 apa: Browning, T. D. (2024). The polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnae066 chicago: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” International Mathematics Research Notices. Oxford University Press, 2024. https://doi.org/10.1093/imrn/rnae066. ieee: T. D. Browning, “The polynomial sieve and equal sums of like polynomials,” International Mathematics Research Notices, vol. 2024, no. 13. Oxford University Press, pp. 10165–10168, 2024. ista: Browning TD. 2024. The polynomial sieve and equal sums of like polynomials. International Mathematics Research Notices. 2024(13), 10165–10168. mla: Browning, Timothy D. “The Polynomial Sieve and Equal Sums of like Polynomials.” International Mathematics Research Notices, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10165–68, doi:10.1093/imrn/rnae066. short: T.D. Browning, International Mathematics Research Notices 2024 (2024) 10165–10168. corr_author: '1' date_created: 2025-02-18T07:15:50Z date_published: 2024-07-01T00:00:00Z date_updated: 2025-09-09T12:16:45Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1093/imrn/rnae066 external_id: isi: - '001196957300001' file: - access_level: open_access checksum: b625b8adf018d2a97591813c1fc17b96 content_type: application/pdf creator: dernst date_created: 2025-02-18T07:56:36Z date_updated: 2025-02-18T07:56:36Z file_id: '19052' file_name: 2024_IMRN_Browning.pdf file_size: 205750 relation: main_file success: 1 file_date_updated: 2025-02-18T07:56:36Z has_accepted_license: '1' intvolume: ' 2024' isi: 1 issue: '13' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: 10165-10168 publication: International Mathematics Research Notices publication_identifier: eissn: - 1687-0247 issn: - 1073-7928 publication_status: published publisher: Oxford University Press quality_controlled: '1' related_material: record: - id: '254' relation: earlier_version status: public scopus_import: '1' status: public title: The polynomial sieve and equal sums of like 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: 2024 year: '2024' ... --- _id: '10018' abstract: - lang: eng text: In order to study integral points of bounded log-anticanonical height on weak del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example, we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove an analogue of Manin's conjecture for integral points with respect to its singularities and its lines. acknowledgement: The first author was partly supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft. The second author was partly supported by FWF grant P 32428-N35 and conducted part of this work as a guest at the Institut de Mathématiques de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Ulrich full_name: Derenthal, Ulrich last_name: Derenthal - first_name: Florian Alexander full_name: Wilsch, Florian Alexander id: 560601DA-8D36-11E9-A136-7AC1E5697425 last_name: Wilsch orcid: 0000-0001-7302-8256 citation: ama: Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. 2024;23(3):1259-1294. doi:10.1017/S1474748022000482 apa: Derenthal, U., & Wilsch, F. A. (2024). Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. Cambridge University Press. https://doi.org/10.1017/S1474748022000482 chicago: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” Journal of the Institute of Mathematics of Jussieu. Cambridge University Press, 2024. https://doi.org/10.1017/S1474748022000482. ieee: U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,” Journal of the Institute of Mathematics of Jussieu, vol. 23, no. 3. Cambridge University Press, pp. 1259–1294, 2024. ista: Derenthal U, Wilsch FA. 2024. Integral points on singular del Pezzo surfaces. Journal of the Institute of Mathematics of Jussieu. 23(3), 1259–1294. mla: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular Del Pezzo Surfaces.” Journal of the Institute of Mathematics of Jussieu, vol. 23, no. 3, Cambridge University Press, 2024, pp. 1259–94, doi:10.1017/S1474748022000482. short: U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu 23 (2024) 1259–1294. corr_author: '1' date_created: 2021-09-15T10:06:48Z date_published: 2024-05-10T00:00:00Z date_updated: 2025-04-15T07:39:01Z day: '10' ddc: - '510' department: - _id: TiBr doi: 10.1017/S1474748022000482 external_id: arxiv: - '2109.06778' isi: - '000881319200001' file: - access_level: open_access checksum: c4698ea12cfe10ef2c6c79880290c7ac content_type: application/pdf creator: dernst date_created: 2024-06-03T08:33:29Z date_updated: 2024-06-03T08:33:29Z file_id: '17102' file_name: 2024_JourMathJussieu_Derenthal.pdf file_size: 592305 relation: main_file success: 1 file_date_updated: 2024-06-03T08:33:29Z has_accepted_license: '1' intvolume: ' 23' isi: 1 issue: '3' keyword: - Integral points - del Pezzo surface - universal torsor - Manin’s conjecture language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 1259-1294 project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Journal of the Institute of Mathematics of Jussieu publication_identifier: eissn: - '1475-3030 ' issn: - 1474-7480 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Integral points on singular del Pezzo surfaces 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: 23 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '17323' 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. 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. article_number: e12269 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 - 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. Strong divisibility sequences and sieve methods. Mathematika. 2024;70(4). doi:10.1112/mtk.12269 apa: Browning, T. D., & Verzobio, M. (2024). Strong divisibility sequences and sieve methods. Mathematika. London Mathematical Society. https://doi.org/10.1112/mtk.12269 chicago: Browning, Timothy D, and Matteo Verzobio. “Strong Divisibility Sequences and Sieve Methods.” Mathematika. London Mathematical Society, 2024. https://doi.org/10.1112/mtk.12269. ieee: T. D. Browning and M. Verzobio, “Strong divisibility sequences and sieve methods,” Mathematika, vol. 70, no. 4. London Mathematical Society, 2024. 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.” Mathematika, vol. 70, no. 4, e12269, London Mathematical Society, 2024, doi:10.1112/mtk.12269. short: T.D. Browning, M. Verzobio, Mathematika 70 (2024). corr_author: '1' date_created: 2024-07-28T22:01:08Z date_published: 2024-10-01T00:00:00Z date_updated: 2025-09-08T08:44:11Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1112/mtk.12269 ec_funded: 1 external_id: isi: - '001273912800001' file: - access_level: open_access checksum: 0b1518bdc1a901413005c19202cfa497 content_type: application/pdf creator: dernst date_created: 2025-01-13T11:06:25Z date_updated: 2025-01-13T11:06:25Z file_id: '18842' file_name: 2024_Mathematika_Browning.pdf file_size: 273006 relation: main_file success: 1 file_date_updated: 2025-01-13T11:06:25Z has_accepted_license: '1' intvolume: ' 70' isi: 1 issue: '4' language: - iso: eng month: '10' 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: Mathematika publication_identifier: eissn: - 2041-7942 issn: - 0025-5793 publication_status: published publisher: London Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Strong divisibility sequences and sieve methods 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: 70 year: '2024' ... --- _id: '17447' abstract: - lang: eng text: Let F be a diagonal cubic form over Z in six variables. From the dual variety in the delta method of Duke–Friedlander–Iwaniec and Heath‐Brown, we unconditionally extract a weighted count of certain special integral zeros of F in regions of diameter X - 8 . Heath‐Brown did the same in four variables, but our analysis differs and captures some novel features. We also put forth an axiomatic framework for more general F. acknowledgement: This paper is an important component of the thesis work described in [25]; many of my acknowledgements there apply here as well. I also thank my advisor, Peter Sarnak, for many helpful suggestions and questions on the exposition, references, assumptions, and scope of (various drafts of) the present work. I am also grateful to Trevor Wooley for providing some helpful general comments on special subvarieties and the reference [24]. I thank Tim Browning for inspiring part of the current title of the paper. Finally, thanks are due to the referee for providing many helpful suggestions. 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 AgreementNo. 101034413. article_number: e12975 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. Special cubic zeros and the dual variety. Journal of the London Mathematical Society. 2024;110(3). doi:10.1112/jlms.12975 apa: Wang, V. (2024). Special cubic zeros and the dual variety. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12975 chicago: Wang, Victor. “Special Cubic Zeros and the Dual Variety.” Journal of the London Mathematical Society. Wiley, 2024. https://doi.org/10.1112/jlms.12975. ieee: V. Wang, “Special cubic zeros and the dual variety,” Journal of the London Mathematical Society, vol. 110, no. 3. Wiley, 2024. ista: Wang V. 2024. Special cubic zeros and the dual variety. Journal of the London Mathematical Society. 110(3), e12975. mla: Wang, Victor. “Special Cubic Zeros and the Dual Variety.” Journal of the London Mathematical Society, vol. 110, no. 3, e12975, Wiley, 2024, doi:10.1112/jlms.12975. short: V. Wang, Journal of the London Mathematical Society 110 (2024). corr_author: '1' date_created: 2024-08-20T08:41:40Z date_published: 2024-08-14T00:00:00Z date_updated: 2025-09-08T08:58:20Z day: '14' ddc: - '512' department: - _id: TiBr doi: 10.1112/jlms.12975 ec_funded: 1 external_id: arxiv: - '2108.03396' isi: - '001310529600001' file: - access_level: open_access checksum: 90437e19f57520b4d66ca62408f6c81e content_type: application/pdf creator: dernst date_created: 2024-08-21T06:36:40Z date_updated: 2024-08-21T06:36:40Z file_id: '17454' file_name: 2024_JourLondonMathSoc_Wang.pdf file_size: 438751 relation: main_file success: 1 file_date_updated: 2024-08-21T06:36:40Z has_accepted_license: '1' intvolume: ' 110' isi: 1 issue: '3' language: - iso: eng month: '08' 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: Journal of the London Mathematical Society publication_identifier: eissn: - 1469-7750 issn: - 0024-6107 publication_status: published publisher: Wiley quality_controlled: '1' scopus_import: '1' status: public title: Special cubic zeros and the dual variety 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: 110 year: '2024' ... --- OA_place: publisher OA_type: hybrid _id: '18064' abstract: - lang: eng text: " We show that the total number of non-torsion integral points on the elliptic curves ED : y\r\n2 = x3 − D2x, where D ranges over positive squarefree integers less than N, is O(N(log N)\r\n−1/4+ǫ). The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of Heath-Brown’s method on estimating the average size of the 2-Selmer group of the curves in this family." article_number: '109946' article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - 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: Chan S. The average number of integral points on the congruent number curves. Advances in Mathematics. 2024;457(11). doi:10.1016/j.aim.2024.109946 apa: Chan, S. (2024). The average number of integral points on the congruent number curves. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2024.109946 chicago: Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” Advances in Mathematics. Elsevier, 2024. https://doi.org/10.1016/j.aim.2024.109946. ieee: S. Chan, “The average number of integral points on the congruent number curves,” Advances in Mathematics, vol. 457, no. 11. Elsevier, 2024. ista: Chan S. 2024. The average number of integral points on the congruent number curves. Advances in Mathematics. 457(11), 109946. mla: Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” Advances in Mathematics, vol. 457, no. 11, 109946, Elsevier, 2024, doi:10.1016/j.aim.2024.109946. short: S. Chan, Advances in Mathematics 457 (2024). corr_author: '1' date_created: 2024-09-15T22:01:39Z date_published: 2024-11-01T00:00:00Z date_updated: 2025-01-13T08:54:36Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1016/j.aim.2024.109946 external_id: arxiv: - '2112.01615' file: - access_level: open_access checksum: f555742540ad91a3040aeafd68b1fcde content_type: application/pdf creator: dernst date_created: 2025-01-13T08:54:09Z date_updated: 2025-01-13T08:54:09Z file_id: '18829' file_name: 2024_AdvancesMath_Chan.pdf file_size: 564386 relation: main_file success: 1 file_date_updated: 2025-01-13T08:54:09Z has_accepted_license: '1' intvolume: ' 457' issue: '11' language: - iso: eng month: '11' oa: 1 oa_version: Published Version publication: Advances in Mathematics publication_identifier: eissn: - 1090-2082 issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: The average number of integral points on the congruent number curves 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: 457 year: '2024' ...