--- _id: '12916' abstract: - lang: eng text: "We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend on the coefficients of the polynomial defining the surface.\r\n" article_processing_charge: No 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 citation: ama: Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 2023;24(1):173-204. doi:10.2422/2036-2145.202010_018 apa: Bonolis, D., & Browning, T. D. (2023). Uniform bounds for rational points on hyperelliptic fibrations. Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale. https://doi.org/10.2422/2036-2145.202010_018 chicago: Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze. Scuola Normale Superiore - Edizioni della Normale, 2023. https://doi.org/10.2422/2036-2145.202010_018. ieee: D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic fibrations,” Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204, 2023. ista: Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic fibrations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 24(1), 173–204. mla: Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points on Hyperelliptic Fibrations.” Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della Normale, 2023, pp. 173–204, doi:10.2422/2036-2145.202010_018. short: D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa - Classe Di Scienze 24 (2023) 173–204. date_created: 2023-05-07T22:01:04Z date_published: 2023-02-16T00:00:00Z date_updated: 2023-10-18T06:54:30Z day: '16' department: - _id: TiBr doi: 10.2422/2036-2145.202010_018 external_id: arxiv: - '2007.14182' intvolume: ' 24' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2007.14182 month: '02' oa: 1 oa_version: Preprint page: 173-204 publication: Annali della Scuola Normale Superiore di Pisa - Classe di Scienze publication_identifier: eissn: - 2036-2145 issn: - 0391-173X publication_status: published publisher: Scuola Normale Superiore - Edizioni della Normale quality_controlled: '1' scopus_import: '1' status: public title: Uniform bounds for rational points on hyperelliptic fibrations type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 24 year: '2023' ... --- _id: '9364' abstract: - lang: eng text: 'Let t : Fp → C be a complex valued function on Fp. A classical problem in analytic number theory is bounding the maximum M(t) := max 0≤H

0 there exists a large subset of a ∈ F×p such that for kl a,1,p : x → e((ax+x) / p) we have M(kla,1,p) ≥ (1−ε/√2π + o(1)) log log p, as p→∞. Finally, we prove a result on the growth of the moments of {M (kla,1,p)}a∈F×p. 2020 Mathematics Subject Classification: 11L03, 11T23 (Primary); 14F20, 60F10 (Secondary).' acknowledgement: I am most thankful to my advisor, Emmanuel Kowalski, for suggesting this problem and for his guidance during these years. I also would like to thank Youness Lamzouri for informing me about his work on sum of incomplete Birch sums and Tal Horesh for her suggestions on a previous version of the paper. Finally, I am very grateful to the anonymous referee for their careful reading of the manuscript and their valuable comments. 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 citation: ama: Bonolis D. On the size of the maximum of incomplete Kloosterman sums. Mathematical Proceedings of the Cambridge Philosophical Society. 2022;172(3):563-590. doi:10.1017/S030500412100030X apa: Bonolis, D. (2022). On the size of the maximum of incomplete Kloosterman sums. Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press. https://doi.org/10.1017/S030500412100030X chicago: Bonolis, Dante. “On the Size of the Maximum of Incomplete Kloosterman Sums.” Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, 2022. https://doi.org/10.1017/S030500412100030X. ieee: D. Bonolis, “On the size of the maximum of incomplete Kloosterman sums,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 172, no. 3. Cambridge University Press, pp. 563–590, 2022. ista: Bonolis D. 2022. On the size of the maximum of incomplete Kloosterman sums. Mathematical Proceedings of the Cambridge Philosophical Society. 172(3), 563–590. mla: Bonolis, Dante. “On the Size of the Maximum of Incomplete Kloosterman Sums.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 172, no. 3, Cambridge University Press, 2022, pp. 563–90, doi:10.1017/S030500412100030X. short: D. Bonolis, Mathematical Proceedings of the Cambridge Philosophical Society 172 (2022) 563–590. date_created: 2021-05-02T22:01:29Z date_published: 2022-05-01T00:00:00Z date_updated: 2023-08-02T06:47:48Z day: '01' ddc: - '510' department: - _id: TiBr doi: 10.1017/S030500412100030X external_id: arxiv: - '1811.10563' isi: - '000784421500001' file: - access_level: open_access checksum: 614d2e9b83a78100408e4ee7752a80a8 content_type: application/pdf creator: cchlebak date_created: 2021-12-01T14:01:54Z date_updated: 2021-12-01T14:01:54Z file_id: '10395' file_name: 2021_MathProcCamPhilSoc_Bonolis.pdf file_size: 334064 relation: main_file success: 1 file_date_updated: 2021-12-01T14:01:54Z has_accepted_license: '1' intvolume: ' 172' isi: 1 issue: '3' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 563 - 590 publication: Mathematical Proceedings of the Cambridge Philosophical Society publication_identifier: eissn: - 1469-8064 issn: - 0305-0041 publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: On the size of the maximum of incomplete Kloosterman 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 172 year: '2022' ... --- _id: '10711' abstract: - lang: eng text: In this paper, we investigate the distribution of the maximum of partial sums of families of m -periodic complex-valued functions satisfying certain conditions. We obtain precise uniform estimates for the distribution function of this maximum in a near-optimal range. Our results apply to partial sums of Kloosterman sums and other families of ℓ -adic trace functions, and are as strong as those obtained by Bober, Goldmakher, Granville and Koukoulopoulos for character sums. In particular, we improve on the recent work of the third author for Birch sums. However, unlike character sums, we are able to construct families of m -periodic complex-valued functions which satisfy our conditions, but for which the Pólya–Vinogradov inequality is sharp. acknowledgement: We would like to thank the anonymous referees for carefully reading the paper and for their remarks and suggestions. article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Pascal full_name: Autissier, Pascal last_name: Autissier - first_name: Dante full_name: Bonolis, Dante id: 6A459894-5FDD-11E9-AF35-BB24E6697425 last_name: Bonolis - first_name: Youness full_name: Lamzouri, Youness last_name: Lamzouri citation: ama: Autissier P, Bonolis D, Lamzouri Y. The distribution of the maximum of partial sums of Kloosterman sums and other trace functions. Compositio Mathematica. 2021;157(7):1610-1651. doi:10.1112/s0010437x21007351 apa: Autissier, P., Bonolis, D., & Lamzouri, Y. (2021). The distribution of the maximum of partial sums of Kloosterman sums and other trace functions. Compositio Mathematica. Cambridge University Press. https://doi.org/10.1112/s0010437x21007351 chicago: Autissier, Pascal, Dante Bonolis, and Youness Lamzouri. “The Distribution of the Maximum of Partial Sums of Kloosterman Sums and Other Trace Functions.” Compositio Mathematica. Cambridge University Press, 2021. https://doi.org/10.1112/s0010437x21007351. ieee: P. Autissier, D. Bonolis, and Y. Lamzouri, “The distribution of the maximum of partial sums of Kloosterman sums and other trace functions,” Compositio Mathematica, vol. 157, no. 7. Cambridge University Press, pp. 1610–1651, 2021. ista: Autissier P, Bonolis D, Lamzouri Y. 2021. The distribution of the maximum of partial sums of Kloosterman sums and other trace functions. Compositio Mathematica. 157(7), 1610–1651. mla: Autissier, Pascal, et al. “The Distribution of the Maximum of Partial Sums of Kloosterman Sums and Other Trace Functions.” Compositio Mathematica, vol. 157, no. 7, Cambridge University Press, 2021, pp. 1610–51, doi:10.1112/s0010437x21007351. short: P. Autissier, D. Bonolis, Y. Lamzouri, Compositio Mathematica 157 (2021) 1610–1651. date_created: 2022-02-01T08:10:43Z date_published: 2021-06-28T00:00:00Z date_updated: 2023-08-17T06:59:16Z day: '28' department: - _id: TiBr doi: 10.1112/s0010437x21007351 external_id: arxiv: - '1909.03266' isi: - '000667289300001' intvolume: ' 157' isi: 1 issue: '7' keyword: - Algebra and Number Theory language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1909.03266 month: '06' oa: 1 oa_version: Preprint page: 1610-1651 publication: Compositio Mathematica publication_identifier: eissn: - 1570-5846 issn: - 0010-437X publication_status: published publisher: Cambridge University Press quality_controlled: '1' status: public title: The distribution of the maximum of partial sums of Kloosterman sums and other trace functions type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 157 year: '2021' ...