--- OA_place: repository OA_type: green _id: '22190' abstract: - lang: eng text: "We consider the set of \U0001D45A×\U0001D45B matrices with rational entries having numerator and denominator of size at most H and obtain various upper bounds on the number of such matrices of a given rank, or with a given determinant, or a given characteristic polynomial. We also consider similar questions for matrices whose entries are Egyptian fractions." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Muhammad full_name: Afifurrahman, Muhammad last_name: Afifurrahman - first_name: Vivian Zieve full_name: Kuperberg, Vivian Zieve id: c3bac823-112d-11f0-a3f5-c264f852e697 last_name: Kuperberg - first_name: Alina full_name: Ostafe, Alina last_name: Ostafe - first_name: Igor E. full_name: Shparlinski, Igor E. last_name: Shparlinski citation: ama: Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. 2024;37(4). doi:10.1515/forum-2024-0114 apa: Afifurrahman, M., Kuperberg, V. Z., Ostafe, A., & Shparlinski, I. E. (2024). Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2024-0114 chicago: Afifurrahman, Muhammad, Vivian Zieve Kuperberg, Alina Ostafe, and Igor E. Shparlinski. “Statistics of Ranks, Determinants and Characteristic Polynomials of Rational Matrices.” Forum Mathematicum. De Gruyter, 2024. https://doi.org/10.1515/forum-2024-0114. ieee: M. Afifurrahman, V. Z. Kuperberg, A. Ostafe, and I. E. Shparlinski, “Statistics of ranks, determinants and characteristic polynomials of rational matrices,” Forum Mathematicum, vol. 37, no. 4. De Gruyter, 2024. ista: Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. 2024. Statistics of ranks, determinants and characteristic polynomials of rational matrices. Forum Mathematicum. 37(4). mla: Afifurrahman, Muhammad, et al. “Statistics of Ranks, Determinants and Characteristic Polynomials of Rational Matrices.” Forum Mathematicum, vol. 37, no. 4, De Gruyter, 2024, doi:10.1515/forum-2024-0114. short: M. Afifurrahman, V.Z. Kuperberg, A. Ostafe, I.E. Shparlinski, Forum Mathematicum 37 (2024). date_created: 2026-06-29T12:55:47Z date_published: 2024-01-01T00:00:00Z date_updated: 2026-07-14T10:48:41Z doi: 10.1515/forum-2024-0114 extern: '1' external_id: arxiv: - '2401.10086' intvolume: ' 37' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2401.10086 mathsc: - 11C20 - 15B36 - 15B52 month: '01' oa: 1 oa_version: Preprint publication: Forum Mathematicum publication_identifier: eissn: - 1435-5337 issn: - 0933-7741 publication_status: published publisher: De Gruyter quality_controlled: '1' scopus_import: '1' status: public title: Statistics of ranks, determinants and characteristic polynomials of rational matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 37 year: '2024' ... --- OA_place: repository OA_type: green _id: '22194' abstract: - lang: eng text: "In [J. P. Keating, B. Rodgers, E. Roditty-Gershon and Z. Rudnick, Sums of divisor functions in \U0001D53D\U0001D45E⁢[\U0001D461] and matrix integrals, Math. Z. 288 2018, 1–2, 167–198], the authors established relationships of the mean-square of sums of the divisor function \U0001D451\U0001D458⁢(\U0001D453) over short intervals and over arithmetic progressions for the function field \U0001D53D\U0001D45E⁢[\U0001D447] to certain integrals over the ensemble of unitary matrices. We consider similar problems leading to distributions over the ensemble of symplectic matrices. We also consider analogous questions involving convolutions of the von Mangoldt function." article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Vivian Zieve full_name: Kuperberg, Vivian Zieve id: c3bac823-112d-11f0-a3f5-c264f852e697 last_name: Kuperberg - first_name: Matilde full_name: Lalín, Matilde last_name: Lalín citation: ama: "Kuperberg VZ, Lalín M. Sums of divisor functions and von Mangoldt convolutions in \U0001D53Dq[T] leading to symplectic distributions. Forum Mathematicum. 2022;34(3):711-747. doi:10.1515/forum-2021-0171" apa: "Kuperberg, V. Z., & Lalín, M. (2022). Sums of divisor functions and von Mangoldt convolutions in \U0001D53Dq[T] leading to symplectic distributions. Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2021-0171" chicago: "Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions and von Mangoldt Convolutions in \U0001D53Dq[T] Leading to Symplectic Distributions.” Forum Mathematicum. De Gruyter, 2022. https://doi.org/10.1515/forum-2021-0171." ieee: "V. Z. Kuperberg and M. Lalín, “Sums of divisor functions and von Mangoldt convolutions in \U0001D53Dq[T] leading to symplectic distributions,” Forum Mathematicum, vol. 34, no. 3. De Gruyter, pp. 711–747, 2022." ista: "Kuperberg VZ, Lalín M. 2022. Sums of divisor functions and von Mangoldt convolutions in \U0001D53Dq[T] leading to symplectic distributions. Forum Mathematicum. 34(3), 711–747." mla: "Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions and von Mangoldt Convolutions in \U0001D53Dq[T] Leading to Symplectic Distributions.” Forum Mathematicum, vol. 34, no. 3, De Gruyter, 2022, pp. 711–47, doi:10.1515/forum-2021-0171." short: V.Z. Kuperberg, M. Lalín, Forum Mathematicum 34 (2022) 711–747. date_created: 2026-06-29T12:57:26Z date_published: 2022-03-26T00:00:00Z date_updated: 2026-07-14T11:02:45Z day: '26' doi: 10.1515/forum-2021-0171 extern: '1' external_id: arxiv: - '2107.01437' intvolume: ' 34' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.2107.01437 month: '03' oa: 1 oa_version: Preprint page: 711-747 publication: Forum Mathematicum publication_identifier: eissn: - 1435-5337 issn: - 0933-7741 publication_status: published publisher: De Gruyter quality_controlled: '1' scopus_import: '1' status: public title: "Sums of divisor functions and von Mangoldt convolutions in \U0001D53Dq[T] leading to symplectic distributions" type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 34 year: '2022' ... --- _id: '8742' abstract: - lang: eng text: We develop a version of Ekedahl’s geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros. 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: Roger full_name: Heath-Brown, Roger last_name: Heath-Brown citation: ama: Browning TD, Heath-Brown R. The geometric sieve for quadrics. Forum Mathematicum. 2021;33(1):147-165. doi:10.1515/forum-2020-0074 apa: Browning, T. D., & Heath-Brown, R. (2021). The geometric sieve for quadrics. Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2020-0074 chicago: Browning, Timothy D, and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” Forum Mathematicum. De Gruyter, 2021. https://doi.org/10.1515/forum-2020-0074. ieee: T. D. Browning and R. Heath-Brown, “The geometric sieve for quadrics,” Forum Mathematicum, vol. 33, no. 1. De Gruyter, pp. 147–165, 2021. ista: Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum Mathematicum. 33(1), 147–165. mla: Browning, Timothy D., and Roger Heath-Brown. “The Geometric Sieve for Quadrics.” Forum Mathematicum, vol. 33, no. 1, De Gruyter, 2021, pp. 147–65, doi:10.1515/forum-2020-0074. short: T.D. Browning, R. Heath-Brown, Forum Mathematicum 33 (2021) 147–165. date_created: 2020-11-08T23:01:25Z date_published: 2021-01-01T00:00:00Z date_updated: 2025-04-15T07:39:01Z day: '01' department: - _id: TiBr doi: 10.1515/forum-2020-0074 external_id: arxiv: - '2003.09593' isi: - '000604750900008' intvolume: ' 33' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2003.09593 month: '01' oa: 1 oa_version: Preprint page: 147-165 project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Forum Mathematicum publication_identifier: eissn: - 1435-5337 issn: - 0933-7741 publication_status: published publisher: De Gruyter quality_controlled: '1' scopus_import: '1' status: public title: The geometric sieve for quadrics type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 33 year: '2021' ... --- OA_place: repository OA_type: green _id: '257' abstract: - lang: eng text: For suitable pairs of diagonal quadratic forms in eight variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares. acknowledgement: While working on this paper the first author was supported by ERC grant 306457 and the second author was supported by SwarnaJayanti Fellowship 2011–12, DST, Government of India. 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: Ritabrata full_name: Munshi, Ritabrata last_name: Munshi citation: ama: Browning TD, Munshi R. Pairs of diagonal quadratic forms and linear correlations among sums of two squares. Forum Mathematicum. 2015;27(4):2025-2050. doi:10.1515/forum-2013-6024 apa: Browning, T. D., & Munshi, R. (2015). Pairs of diagonal quadratic forms and linear correlations among sums of two squares. Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2013-6024 chicago: Browning, Timothy D, and Ritabrata Munshi. “Pairs of Diagonal Quadratic Forms and Linear Correlations among Sums of Two Squares.” Forum Mathematicum. De Gruyter, 2015. https://doi.org/10.1515/forum-2013-6024. ieee: T. D. Browning and R. Munshi, “Pairs of diagonal quadratic forms and linear correlations among sums of two squares,” Forum Mathematicum, vol. 27, no. 4. De Gruyter, pp. 2025–2050, 2015. ista: Browning TD, Munshi R. 2015. Pairs of diagonal quadratic forms and linear correlations among sums of two squares. Forum Mathematicum. 27(4), 2025–2050. mla: Browning, Timothy D., and Ritabrata Munshi. “Pairs of Diagonal Quadratic Forms and Linear Correlations among Sums of Two Squares.” Forum Mathematicum, vol. 27, no. 4, De Gruyter, 2015, pp. 2025–50, doi:10.1515/forum-2013-6024. short: T.D. Browning, R. Munshi, Forum Mathematicum 27 (2015) 2025–2050. date_created: 2018-12-11T11:45:28Z date_published: 2015-07-10T00:00:00Z date_updated: 2026-05-19T13:08:06Z day: '10' doi: 10.1515/forum-2013-6024 extern: '1' external_id: arxiv: - '1302.2434' intvolume: ' 27' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1302.2434 month: '07' oa: 1 oa_version: Preprint page: 2025 - 2050 publication: Forum Mathematicum publication_identifier: eissn: - 1435-5337 issn: - 0933-7741 publication_status: published publisher: De Gruyter publist_id: '7645' quality_controlled: '1' scopus_import: '1' status: public title: Pairs of diagonal quadratic forms and linear correlations among sums of two squares type: journal_article user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd volume: 27 year: '2015' ... --- OA_place: repository OA_type: green _id: '22049' abstract: - lang: eng text: 'We consider the minimal mass m0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + Δu = μ|u|^4/d u to blow up. If m0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in is compact after quotienting out by the symmetries of the equation. A similar result is obtained for spherically symmetric solutions. Similar results were previously obtained by Keraani, [Keraani S.: On the blow-up phenomenon of the critical nonlinear Schrödinger equation. J. Funct. Anal. 235 (2006), 171–192], in dimensions 1, 2 and Begout and Vargas, [Begout P., Vargas A.: Mass concentration phenomena for the L2-critical nonlinear Schrödinger equation, preprint], in dimensions d ≥ 3 for the mass-critical NLS and by Kenig and Merle, [Kenig C., Merle F.: Global well-posedness, scattering, and blowup for the energy-critical, focusing, non-linear Schrödinger equation in the radial case, preprint], in the energy-critical case. In a subsequent paper we shall use this compactness result to establish global existence and scattering in for the defocusing NLS in three and higher dimensions with spherically symmetric data.' article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Terence full_name: Tao, Terence last_name: Tao - first_name: Monica full_name: Visan, Monica id: 056daca0-b8d1-11f0-964f-f91054abf8ca last_name: Visan - first_name: Xiaoyi full_name: Zhang, Xiaoyi last_name: Zhang citation: ama: Tao T, Vişan M, Zhang X. Minimal-mass blowup solutions of the mass-critical NLS. Forum Mathematicum. 2008;20(5):881-919. doi:10.1515/forum.2008.042 apa: Tao, T., Vişan, M., & Zhang, X. (2008). Minimal-mass blowup solutions of the mass-critical NLS. Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum.2008.042 chicago: Tao, Terence, Monica Vişan, and Xiaoyi Zhang. “Minimal-Mass Blowup Solutions of the Mass-Critical NLS.” Forum Mathematicum. De Gruyter, 2008. https://doi.org/10.1515/forum.2008.042. ieee: T. Tao, M. Vişan, and X. Zhang, “Minimal-mass blowup solutions of the mass-critical NLS,” Forum Mathematicum, vol. 20, no. 5. De Gruyter, pp. 881–919, 2008. ista: Tao T, Vişan M, Zhang X. 2008. Minimal-mass blowup solutions of the mass-critical NLS. Forum Mathematicum. 20(5), 881–919. mla: Tao, Terence, et al. “Minimal-Mass Blowup Solutions of the Mass-Critical NLS.” Forum Mathematicum, vol. 20, no. 5, De Gruyter, 2008, pp. 881–919, doi:10.1515/forum.2008.042. short: T. Tao, M. Vişan, X. Zhang, Forum Mathematicum 20 (2008) 881–919. das_tickbox: '1' date_created: 2026-06-19T07:53:12Z date_published: 2008-11-03T00:00:00Z date_updated: 2026-06-25T08:15:22Z day: '03' doi: 10.1515/forum.2008.042 extern: '1' external_id: arxiv: - math/0609690 intvolume: ' 20' issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.math/0609690 mathsc: - 35Q55 month: '11' oa: 1 oa_version: Preprint page: 881-919 publication: Forum Mathematicum publication_identifier: eissn: - 1435-5337 issn: - 0933-7741 publication_status: published publisher: De Gruyter quality_controlled: '1' scopus_import: '1' status: public title: Minimal-mass blowup solutions of the mass-critical NLS type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 20 year: '2008' ...