--- _id: '13180' abstract: - lang: eng text: We study the density of everywhere locally soluble diagonal quadric surfaces, parameterised by rational points that lie on a split quadric surface article_processing_charge: No 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: Julian full_name: Lyczak, Julian id: 3572849A-F248-11E8-B48F-1D18A9856A87 last_name: Lyczak - first_name: Roman full_name: Sarapin, Roman last_name: Sarapin citation: ama: Browning TD, Lyczak J, Sarapin R. Local solubility for a family of quadrics over a split quadric surface. Involve. 2023;16(2):331-342. doi:10.2140/involve.2023.16.331 apa: Browning, T. D., Lyczak, J., & Sarapin, R. (2023). Local solubility for a family of quadrics over a split quadric surface. Involve. Mathematical Sciences Publishers. https://doi.org/10.2140/involve.2023.16.331 chicago: Browning, Timothy D, Julian Lyczak, and Roman Sarapin. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” Involve. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/involve.2023.16.331. ieee: T. D. Browning, J. Lyczak, and R. Sarapin, “Local solubility for a family of quadrics over a split quadric surface,” Involve, vol. 16, no. 2. Mathematical Sciences Publishers, pp. 331–342, 2023. ista: Browning TD, Lyczak J, Sarapin R. 2023. Local solubility for a family of quadrics over a split quadric surface. Involve. 16(2), 331–342. mla: Browning, Timothy D., et al. “Local Solubility for a Family of Quadrics over a Split Quadric Surface.” Involve, vol. 16, no. 2, Mathematical Sciences Publishers, 2023, pp. 331–42, doi:10.2140/involve.2023.16.331. short: T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 331–342. date_created: 2023-07-02T22:00:43Z date_published: 2023-05-26T00:00:00Z date_updated: 2023-07-17T08:39:19Z day: '26' department: - _id: TiBr doi: 10.2140/involve.2023.16.331 external_id: arxiv: - '2203.06881' intvolume: ' 16' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2203.06881 month: '05' oa: 1 oa_version: Preprint page: 331-342 publication: Involve publication_identifier: eissn: - 1944-4184 issn: - 1944-4176 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Local solubility for a family of quadrics over a split quadric surface type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2023' ... --- _id: '13091' abstract: - lang: eng text: We use a function field version of the Hardy–Littlewood circle method to study the locus of free rational curves on an arbitrary smooth projective hypersurface of sufficiently low degree. On the one hand this allows us to bound the dimension of the singular locus of the moduli space of rational curves on such hypersurfaces and, on the other hand, it sheds light on Peyre’s reformulation of the Batyrev–Manin conjecture in terms of slopes with respect to the tangent bundle. acknowledgement: The authors are grateful to Paul Nelson, Per Salberger and Jason Starr for useful comments. While working on this paper the first author was supported by EPRSC grant EP/P026710/1. The research was partially conducted during the period the second author served as a Clay Research Fellow, and partially conducted during the period he was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation. article_processing_charge: No 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: Will full_name: Sawin, Will last_name: Sawin citation: ama: Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 2023;17(3):719-748. doi:10.2140/ant.2023.17.719 apa: Browning, T. D., & Sawin, W. (2023). Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2023.17.719 chicago: Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” Algebra and Number Theory. Mathematical Sciences Publishers, 2023. https://doi.org/10.2140/ant.2023.17.719. ieee: T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces and the circle method,” Algebra and Number Theory, vol. 17, no. 3. Mathematical Sciences Publishers, pp. 719–748, 2023. ista: Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces and the circle method. Algebra and Number Theory. 17(3), 719–748. mla: Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” Algebra and Number Theory, vol. 17, no. 3, Mathematical Sciences Publishers, 2023, pp. 719–48, doi:10.2140/ant.2023.17.719. short: T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 719–748. date_created: 2023-05-28T22:01:02Z date_published: 2023-04-12T00:00:00Z date_updated: 2023-08-01T14:51:57Z day: '12' ddc: - '510' department: - _id: TiBr doi: 10.2140/ant.2023.17.719 external_id: arxiv: - '1810.06882' isi: - '000996014700004' file: - access_level: open_access checksum: 5d5d67b235905650e33cf7065d7583b4 content_type: application/pdf creator: dernst date_created: 2023-05-30T08:05:22Z date_updated: 2023-05-30T08:05:22Z file_id: '13101' file_name: 2023_AlgebraNumberTheory_Browning.pdf file_size: 1430719 relation: main_file success: 1 file_date_updated: 2023-05-30T08:05:22Z has_accepted_license: '1' intvolume: ' 17' isi: 1 issue: '3' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 719-748 project: - _id: 26A8D266-B435-11E9-9278-68D0E5697425 grant_number: EP-P026710-2 name: Between rational and integral points publication: Algebra and Number Theory publication_identifier: eissn: - 1944-7833 issn: - 1937-0652 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Free rational 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: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 17 year: '2023' ... --- _id: '8682' abstract: - lang: eng text: It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least 3 over any number field. Moreover, for such varieties it follows from a general conjecture of Colliot-Thélène that the Brauer--Manin obstruction to the Hasse principle should be the only one, so that the Hasse principle is expected to hold. Working over the field of rational numbers and ordering Fano hypersurfaces of fixed degree and dimension by height, we prove that almost every such hypersurface satisfies the Hasse principle provided that the dimension is at least 3. This proves a conjecture of Poonen and Voloch in every case except for cubic surfaces. article_processing_charge: No 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: Pierre Le full_name: Boudec, Pierre Le last_name: Boudec - first_name: Will full_name: Sawin, Will last_name: Sawin citation: ama: Browning TD, Boudec PL, Sawin W. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 2023;197(3):1115-1203. doi:10.4007/annals.2023.197.3.3 apa: Browning, T. D., Boudec, P. L., & Sawin, W. (2023). The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. Princeton University. https://doi.org/10.4007/annals.2023.197.3.3 chicago: Browning, Timothy D, Pierre Le Boudec, and Will Sawin. “The Hasse Principle for Random Fano Hypersurfaces.” Annals of Mathematics. Princeton University, 2023. https://doi.org/10.4007/annals.2023.197.3.3. ieee: T. D. Browning, P. L. Boudec, and W. Sawin, “The Hasse principle for random Fano hypersurfaces,” Annals of Mathematics, vol. 197, no. 3. Princeton University, pp. 1115–1203, 2023. ista: Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203. mla: Browning, Timothy D., et al. “The Hasse Principle for Random Fano Hypersurfaces.” Annals of Mathematics, vol. 197, no. 3, Princeton University, 2023, pp. 1115–203, doi:10.4007/annals.2023.197.3.3. short: T.D. Browning, P.L. Boudec, W. Sawin, Annals of Mathematics 197 (2023) 1115–1203. date_created: 2020-10-19T14:28:50Z date_published: 2023-05-01T00:00:00Z date_updated: 2023-10-17T12:47:43Z day: '01' department: - _id: TiBr doi: 10.4007/annals.2023.197.3.3 external_id: arxiv: - '2006.02356' isi: - '000966611000003' intvolume: ' 197' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2006.02356 month: '05' oa: 1 oa_version: Preprint page: 1115-1203 publication: Annals of Mathematics publication_identifier: issn: - 0003-486X publication_status: published publisher: Princeton University quality_controlled: '1' related_material: link: - description: News on IST Homepage relation: press_release url: https://ist.ac.at/en/news/when-is-necessary-sufficient/ status: public title: The Hasse principle for random Fano hypersurfaces type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 197 year: '2023' ... --- _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 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: '9199' abstract: - lang: eng text: "We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre's programme on \"freeness\" for rational points of bounded height on Fano\r\nvarieties." acknowledgement: The authors are very grateful to Will Sawin for useful remarks about this topic. While working on this paper the first two authors were supported by EPSRC grant EP/P026710/1, and the first and last authors by FWF grant P 32428-N35. article_processing_charge: No 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: Tal full_name: Horesh, Tal id: C8B7BF48-8D81-11E9-BCA9-F536E6697425 last_name: Horesh - 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, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians. Algebra & Number Theory. 2022;16(10):2385-2407. doi:10.2140/ant.2022.16.2385 apa: Browning, T. D., Horesh, T., & Wilsch, F. A. (2022). Equidistribution and freeness on Grassmannians. Algebra & Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2022.16.2385 chicago: Browning, Timothy D, Tal Horesh, and Florian Alexander Wilsch. “Equidistribution and Freeness on Grassmannians.” Algebra & Number Theory. Mathematical Sciences Publishers, 2022. https://doi.org/10.2140/ant.2022.16.2385. ieee: T. D. Browning, T. Horesh, and F. A. Wilsch, “Equidistribution and freeness on Grassmannians,” Algebra & Number Theory, vol. 16, no. 10. Mathematical Sciences Publishers, pp. 2385–2407, 2022. ista: Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians. Algebra & Number Theory. 16(10), 2385–2407. mla: Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.” Algebra & Number Theory, vol. 16, no. 10, Mathematical Sciences Publishers, 2022, pp. 2385–407, doi:10.2140/ant.2022.16.2385. short: T.D. Browning, T. Horesh, F.A. Wilsch, Algebra & Number Theory 16 (2022) 2385–2407. date_created: 2021-02-25T09:56:57Z date_published: 2022-12-01T00:00:00Z date_updated: 2023-08-02T06:46:38Z day: '01' department: - _id: TiBr doi: 10.2140/ant.2022.16.2385 external_id: arxiv: - '2102.11552' isi: - '000961514100004' intvolume: ' 16' isi: 1 issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2102.11552 month: '12' oa: 1 oa_version: Preprint page: 2385-2407 project: - _id: 26A8D266-B435-11E9-9278-68D0E5697425 grant_number: EP-P026710-2 name: Between rational and integral points - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: Algebra & Number Theory publication_identifier: eissn: - 1944-7833 issn: - 1937-0652 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Equidistribution and freeness on Grassmannians type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 16 year: '2022' ... --- _id: '12776' abstract: - lang: eng text: An improved asymptotic formula is established for the number of rational points of bounded height on the split smooth del Pezzo surface of degree 5. The proof uses the five conic bundle structures on the surface. acknowledgement: This work was begun while the author was participating in the programme on "Diophantine equations" at the Hausdorff Research Institute for Mathematics in Bonn in 2009. The hospitality and financial support of the institute is gratefully acknowledged. The idea of using conic bundles to study the split del Pezzo surface of degree 5 was explained to the author by Professor Salberger. The author is very grateful to him for his input into this project and also to Shuntaro Yamagishi for many useful comments on an earlier version of this manuscript. While working on this paper the author was supported by FWF grant P32428-N35. article_processing_charge: No 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. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 2022;28:1193-1229. apa: Browning, T. D. (2022). Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. State University of New York. chicago: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” New York Journal of Mathematics. State University of New York, 2022. ieee: T. D. Browning, “Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5,” New York Journal of Mathematics, vol. 28. State University of New York, pp. 1193–1229, 2022. ista: Browning TD. 2022. Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5. New York Journal of Mathematics. 28, 1193–1229. mla: Browning, Timothy D. “Revisiting the Manin–Peyre Conjecture for the Split Del Pezzo Surface of Degree 5.” New York Journal of Mathematics, vol. 28, State University of New York, 2022, pp. 1193–229. short: T.D. Browning, New York Journal of Mathematics 28 (2022) 1193–1229. date_created: 2023-03-28T09:21:09Z date_published: 2022-08-24T00:00:00Z date_updated: 2023-10-18T07:59:13Z day: '24' ddc: - '510' department: - _id: TiBr file: - access_level: open_access checksum: c01e8291794a1bdb7416aa103cb68ef8 content_type: application/pdf creator: dernst date_created: 2023-03-30T07:09:35Z date_updated: 2023-03-30T07:09:35Z file_id: '12778' file_name: 2022_NYJM_Browning.pdf file_size: 897267 relation: main_file success: 1 file_date_updated: 2023-03-30T07:09:35Z has_accepted_license: '1' intvolume: ' 28' language: - iso: eng month: '08' oa: 1 oa_version: Published Version page: 1193 - 1229 project: - _id: 26AEDAB2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P32428 name: New frontiers of the Manin conjecture publication: New York Journal of Mathematics publication_identifier: issn: - 1076-9803 publication_status: published publisher: State University of New York quality_controlled: '1' status: public title: Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5 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: 28 year: '2022' ... --- _id: '10415' abstract: - lang: eng text: The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties. This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. alternative_title: - Progress in Mathematics article_processing_charge: No 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. Cubic Forms and the Circle Method. Vol 343. Cham: Springer Nature; 2021. doi:10.1007/978-3-030-86872-7' apa: 'Browning, T. D. (2021). Cubic Forms and the Circle Method (Vol. 343). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-86872-7' chicago: 'Browning, Timothy D. Cubic Forms and the Circle Method. Vol. 343. Cham: Springer Nature, 2021. https://doi.org/10.1007/978-3-030-86872-7.' ieee: 'T. D. Browning, Cubic Forms and the Circle Method, vol. 343. Cham: Springer Nature, 2021.' ista: 'Browning TD. 2021. Cubic Forms and the Circle Method, Cham: Springer Nature, XIV, 166p.' mla: Browning, Timothy D. Cubic Forms and the Circle Method. Vol. 343, Springer Nature, 2021, doi:10.1007/978-3-030-86872-7. short: T.D. Browning, Cubic Forms and the Circle Method, Springer Nature, Cham, 2021. date_created: 2021-12-05T23:01:46Z date_published: 2021-12-01T00:00:00Z date_updated: 2022-06-03T07:38:33Z day: '01' department: - _id: TiBr doi: 10.1007/978-3-030-86872-7 intvolume: ' 343' language: - iso: eng month: '12' oa_version: None page: XIV, 166 place: Cham publication_identifier: eisbn: - 978-3-030-86872-7 eissn: - 2296-505X isbn: - 978-3-030-86871-0 issn: - 0743-1643 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Cubic Forms and the Circle Method type: book user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 343 year: '2021' ... --- _id: '9260' abstract: - lang: eng text: We study the density of rational points on a higher-dimensional orbifold (Pn−1,Δ) when Δ is a Q-divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley. acknowledgement: While working on this paper the authors were both supported by EPSRC grant EP/P026710/1, and the second author received additional support from the NWO Veni Grant 016.Veni.192.047. Thanks are due to Marta Pieropan, Arne Smeets and Sho Tanimoto for useful conversations related to this topic, and to the anonymous referee for numerous helpful suggestions. article_processing_charge: No 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: Shuntaro full_name: Yamagishi, Shuntaro last_name: Yamagishi citation: ama: Browning TD, Yamagishi S. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 2021;299:1071–1101. doi:10.1007/s00209-021-02695-w apa: Browning, T. D., & Yamagishi, S. (2021). Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. Springer Nature. https://doi.org/10.1007/s00209-021-02695-w chicago: Browning, Timothy D, and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift. Springer Nature, 2021. https://doi.org/10.1007/s00209-021-02695-w. ieee: T. D. Browning and S. Yamagishi, “Arithmetic of higher-dimensional orbifolds and a mixed Waring problem,” Mathematische Zeitschrift, vol. 299. Springer Nature, pp. 1071–1101, 2021. ista: Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101. mla: Browning, Timothy D., and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” Mathematische Zeitschrift, vol. 299, Springer Nature, 2021, pp. 1071–1101, doi:10.1007/s00209-021-02695-w. short: T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 1071–1101. date_created: 2021-03-21T23:01:21Z date_published: 2021-03-05T00:00:00Z date_updated: 2023-08-07T14:20:00Z day: '05' ddc: - '510' department: - _id: TiBr doi: 10.1007/s00209-021-02695-w external_id: isi: - '000625573800002' file: - access_level: open_access checksum: 8ed9f49568806894744096dbbca0ad7b content_type: application/pdf creator: dernst date_created: 2021-03-22T12:41:26Z date_updated: 2021-03-22T12:41:26Z file_id: '9279' file_name: 2021_MathZeitschrift_Browning.pdf file_size: 492685 relation: main_file success: 1 file_date_updated: 2021-03-22T12:41:26Z has_accepted_license: '1' intvolume: ' 299' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: 1071–1101 project: - _id: 26A8D266-B435-11E9-9278-68D0E5697425 grant_number: EP-P026710-2 name: Between rational and integral points 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: Arithmetic of higher-dimensional orbifolds and a mixed Waring problem 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: 299 year: '2021' ... --- _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 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: 2023-10-17T07:39:01Z 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' ... --- _id: '177' abstract: - lang: eng text: We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree. article_processing_charge: No 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: Will full_name: Sawin, Will last_name: Sawin citation: ama: Browning TD, Sawin W. A geometric version of the circle method. Annals of Mathematics. 2020;191(3):893-948. doi:10.4007/annals.2020.191.3.4 apa: Browning, T. D., & Sawin, W. (2020). A geometric version of the circle method. Annals of Mathematics. Princeton University. https://doi.org/10.4007/annals.2020.191.3.4 chicago: Browning, Timothy D, and Will Sawin. “A Geometric Version of the Circle Method.” Annals of Mathematics. Princeton University, 2020. https://doi.org/10.4007/annals.2020.191.3.4. ieee: T. D. Browning and W. Sawin, “A geometric version of the circle method,” Annals of Mathematics, vol. 191, no. 3. Princeton University, pp. 893–948, 2020. ista: Browning TD, Sawin W. 2020. A geometric version of the circle method. Annals of Mathematics. 191(3), 893–948. mla: Browning, Timothy D., and Will Sawin. “A Geometric Version of the Circle Method.” Annals of Mathematics, vol. 191, no. 3, Princeton University, 2020, pp. 893–948, doi:10.4007/annals.2020.191.3.4. short: T.D. Browning, W. Sawin, Annals of Mathematics 191 (2020) 893–948. date_created: 2018-12-11T11:45:02Z date_published: 2020-05-01T00:00:00Z date_updated: 2023-08-17T07:12:37Z day: '01' department: - _id: TiBr doi: 10.4007/annals.2020.191.3.4 external_id: arxiv: - '1711.10451' isi: - '000526986300004' intvolume: ' 191' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1711.10451 month: '05' oa: 1 oa_version: Preprint page: 893-948 publication: Annals of Mathematics publication_status: published publisher: Princeton University publist_id: '7744' quality_controlled: '1' status: public title: A geometric version of the circle method type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 191 year: '2020' ... --- _id: '9007' abstract: - lang: eng text: Motivated by a recent question of Peyre, we apply the Hardy–Littlewood circle method to count “sufficiently free” rational points of bounded height on arbitrary smooth projective hypersurfaces of low degree that are defined over the rationals. article_processing_charge: No 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: Will full_name: Sawin, Will last_name: Sawin citation: ama: Browning TD, Sawin W. Free rational points on smooth hypersurfaces. Commentarii Mathematici Helvetici. 2020;95(4):635-659. doi:10.4171/CMH/499 apa: Browning, T. D., & Sawin, W. (2020). Free rational points on smooth hypersurfaces. Commentarii Mathematici Helvetici. European Mathematical Society. https://doi.org/10.4171/CMH/499 chicago: Browning, Timothy D, and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.” Commentarii Mathematici Helvetici. European Mathematical Society, 2020. https://doi.org/10.4171/CMH/499. ieee: T. D. Browning and W. Sawin, “Free rational points on smooth hypersurfaces,” Commentarii Mathematici Helvetici, vol. 95, no. 4. European Mathematical Society, pp. 635–659, 2020. ista: Browning TD, Sawin W. 2020. Free rational points on smooth hypersurfaces. Commentarii Mathematici Helvetici. 95(4), 635–659. mla: Browning, Timothy D., and Will Sawin. “Free Rational Points on Smooth Hypersurfaces.” Commentarii Mathematici Helvetici, vol. 95, no. 4, European Mathematical Society, 2020, pp. 635–59, doi:10.4171/CMH/499. short: T.D. Browning, W. Sawin, Commentarii Mathematici Helvetici 95 (2020) 635–659. date_created: 2021-01-17T23:01:11Z date_published: 2020-12-07T00:00:00Z date_updated: 2023-08-24T11:11:36Z day: '07' department: - _id: TiBr doi: 10.4171/CMH/499 external_id: arxiv: - '1906.08463' isi: - '000596833300001' intvolume: ' 95' isi: 1 issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1906.08463 month: '12' oa: 1 oa_version: Preprint page: 635-659 publication: Commentarii Mathematici Helvetici publication_identifier: eissn: - '14208946' issn: - '00102571' publication_status: published publisher: European Mathematical Society quality_controlled: '1' scopus_import: '1' status: public title: Free rational points on smooth hypersurfaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 95 year: '2020' ... --- _id: '179' abstract: - lang: eng text: An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariski dense subset of the biprojective hypersurface x1y21+⋯+x4y24=0 in ℙ3×ℙ3. This confirms the modified Manin conjecture for this variety, in which the removal of a thin set of rational points is allowed. article_processing_charge: No 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: Roger full_name: Heath Brown, Roger last_name: Heath Brown citation: ama: Browning TD, Heath Brown R. Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. 2020;169(16):3099-3165. doi:10.1215/00127094-2020-0031 apa: Browning, T. D., & Heath Brown, R. (2020). Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/00127094-2020-0031 chicago: Browning, Timothy D, and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal. Duke University Press, 2020. https://doi.org/10.1215/00127094-2020-0031. ieee: T. D. Browning and R. Heath Brown, “Density of rational points on a quadric bundle in ℙ3×ℙ3,” Duke Mathematical Journal, vol. 169, no. 16. Duke University Press, pp. 3099–3165, 2020. ista: Browning TD, Heath Brown R. 2020. Density of rational points on a quadric bundle in ℙ3×ℙ3. Duke Mathematical Journal. 169(16), 3099–3165. mla: Browning, Timothy D., and Roger Heath Brown. “Density of Rational Points on a Quadric Bundle in ℙ3×ℙ3.” Duke Mathematical Journal, vol. 169, no. 16, Duke University Press, 2020, pp. 3099–165, doi:10.1215/00127094-2020-0031. short: T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 3099–3165. date_created: 2018-12-11T11:45:02Z date_published: 2020-09-10T00:00:00Z date_updated: 2023-10-17T12:51:10Z day: '10' department: - _id: TiBr doi: 10.1215/00127094-2020-0031 external_id: arxiv: - '1805.10715' isi: - '000582676300002' intvolume: ' 169' isi: 1 issue: '16' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1805.10715 month: '09' oa: 1 oa_version: Preprint page: 3099-3165 publication: Duke Mathematical Journal publication_identifier: issn: - 0012-7094 publication_status: published publisher: Duke University Press quality_controlled: '1' status: public title: Density of rational points on a quadric bundle in ℙ3×ℙ3 type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 169 year: '2020' ... --- _id: '170' abstract: - lang: eng text: Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over ℚ that contains a conic defined over ℚ . 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: Efthymios full_name: Sofos, Efthymios last_name: Sofos citation: ama: Browning TD, Sofos E. Counting rational points on quartic del Pezzo surfaces with a rational conic. Mathematische Annalen. 2019;373(3-4):977-1016. doi:10.1007/s00208-018-1716-6 apa: Browning, T. D., & Sofos, E. (2019). Counting rational points on quartic del Pezzo surfaces with a rational conic. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-018-1716-6 chicago: Browning, Timothy D, and Efthymios Sofos. “Counting Rational Points on Quartic Del Pezzo Surfaces with a Rational Conic.” Mathematische Annalen. Springer Nature, 2019. https://doi.org/10.1007/s00208-018-1716-6. ieee: T. D. Browning and E. Sofos, “Counting rational points on quartic del Pezzo surfaces with a rational conic,” Mathematische Annalen, vol. 373, no. 3–4. Springer Nature, pp. 977–1016, 2019. ista: Browning TD, Sofos E. 2019. Counting rational points on quartic del Pezzo surfaces with a rational conic. Mathematische Annalen. 373(3–4), 977–1016. mla: Browning, Timothy D., and Efthymios Sofos. “Counting Rational Points on Quartic Del Pezzo Surfaces with a Rational Conic.” Mathematische Annalen, vol. 373, no. 3–4, Springer Nature, 2019, pp. 977–1016, doi:10.1007/s00208-018-1716-6. short: T.D. Browning, E. Sofos, Mathematische Annalen 373 (2019) 977–1016. date_created: 2018-12-11T11:44:59Z date_published: 2019-04-01T00:00:00Z date_updated: 2021-01-12T06:52:37Z day: '01' ddc: - '510' doi: 10.1007/s00208-018-1716-6 extern: '1' external_id: arxiv: - '1609.09057' file: - access_level: open_access checksum: 4061dc2fe99bee25d9adf2d2018cf608 content_type: application/pdf creator: dernst date_created: 2019-05-23T07:53:27Z date_updated: 2020-07-14T12:45:12Z file_id: '6479' file_name: 2019_MathAnnalen_Browning.pdf file_size: 712847 relation: main_file file_date_updated: 2020-07-14T12:45:12Z has_accepted_license: '1' intvolume: ' 373' issue: 3-4 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 977-1016 publication: Mathematische Annalen publication_status: published publisher: Springer Nature quality_controlled: '1' status: public title: Counting rational points on quartic del Pezzo surfaces with a rational conic 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: 373 year: '2019' ... --- _id: '175' abstract: - lang: eng text: An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points. article_processing_charge: No 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: Daniel full_name: Loughran, Daniel last_name: Loughran citation: ama: Browning TD, Loughran D. Sieving rational points on varieties. Transactions of the American Mathematical Society. 2019;371(8):5757-5785. doi:10.1090/tran/7514 apa: Browning, T. D., & Loughran, D. (2019). Sieving rational points on varieties. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/7514 chicago: Browning, Timothy D, and Daniel Loughran. “Sieving Rational Points on Varieties.” Transactions of the American Mathematical Society. American Mathematical Society, 2019. https://doi.org/10.1090/tran/7514. ieee: T. D. Browning and D. Loughran, “Sieving rational points on varieties,” Transactions of the American Mathematical Society, vol. 371, no. 8. American Mathematical Society, pp. 5757–5785, 2019. ista: Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions of the American Mathematical Society. 371(8), 5757–5785. mla: Browning, Timothy D., and Daniel Loughran. “Sieving Rational Points on Varieties.” Transactions of the American Mathematical Society, vol. 371, no. 8, American Mathematical Society, 2019, pp. 5757–85, doi:10.1090/tran/7514. short: T.D. Browning, D. Loughran, Transactions of the American Mathematical Society 371 (2019) 5757–5785. date_created: 2018-12-11T11:45:01Z date_published: 2019-04-15T00:00:00Z date_updated: 2023-08-24T14:34:56Z day: '15' department: - _id: TiBr doi: 10.1090/tran/7514 external_id: arxiv: - '1705.01999' isi: - '000464034200019' intvolume: ' 371' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1705.01999 month: '04' oa: 1 oa_version: Preprint page: 5757-5785 publication: Transactions of the American Mathematical Society publication_identifier: eissn: - '10886850' issn: - '00029947' publication_status: published publisher: American Mathematical Society publist_id: '7746' quality_controlled: '1' scopus_import: '1' status: public title: Sieving rational points on varieties type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 371 year: '2019' ... --- _id: '6310' abstract: - lang: eng text: An asymptotic formula is established for the number of rational points of bounded anticanonical height which lie on a certain Zariskiopen subset of an arbitrary smooth biquadratic hypersurface in sufficiently many variables. The proof uses the Hardy–Littlewood circle method. article_processing_charge: No 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: L.Q. full_name: Hu, L.Q. last_name: Hu citation: ama: Browning TD, Hu LQ. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 2019;349:920-940. doi:10.1016/j.aim.2019.04.031 apa: Browning, T. D., & Hu, L. Q. (2019). Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2019.04.031 chicago: Browning, Timothy D, and L.Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” Advances in Mathematics. Elsevier, 2019. https://doi.org/10.1016/j.aim.2019.04.031. ieee: T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,” Advances in Mathematics, vol. 349. Elsevier, pp. 920–940, 2019. ista: Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 349, 920–940. mla: Browning, Timothy D., and L. Q. Hu. “Counting Rational Points on Biquadratic Hypersurfaces.” Advances in Mathematics, vol. 349, Elsevier, 2019, pp. 920–40, doi:10.1016/j.aim.2019.04.031. short: T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940. date_created: 2019-04-16T09:13:25Z date_published: 2019-06-20T00:00:00Z date_updated: 2023-08-25T10:11:55Z day: '20' ddc: - '512' department: - _id: TiBr doi: 10.1016/j.aim.2019.04.031 external_id: arxiv: - '1810.08426' isi: - '000468857300025' file: - access_level: open_access checksum: a63594a3a91b4ba6e2a1b78b0720b3d0 content_type: application/pdf creator: tbrownin date_created: 2019-04-16T09:12:20Z date_updated: 2020-07-14T12:47:27Z file_id: '6311' file_name: wliqun.pdf file_size: 379158 relation: main_file file_date_updated: 2020-07-14T12:47:27Z has_accepted_license: '1' intvolume: ' 349' isi: 1 language: - iso: eng month: '06' oa: 1 oa_version: Submitted Version page: 920-940 publication: Advances in Mathematics publication_identifier: eissn: - '10902082' issn: - '00018708' publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Counting rational points on biquadratic hypersurfaces type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 349 year: '2019' ... --- _id: '174' abstract: - lang: eng text: We survey recent efforts to quantify failures of the Hasse principle in families of rationally connected varieties. alternative_title: - Proceedings of Symposia in Pure Mathematics article_processing_charge: No 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. How often does the Hasse principle hold? In: Vol 97. American Mathematical Society; 2018:89-102. doi:10.1090/pspum/097.2/01700' apa: 'Browning, T. D. (2018). How often does the Hasse principle hold? (Vol. 97, pp. 89–102). Presented at the Algebraic Geometry, Salt Lake City, Utah, USA: American Mathematical Society. https://doi.org/10.1090/pspum/097.2/01700' chicago: Browning, Timothy D. “How Often Does the Hasse Principle Hold?,” 97:89–102. American Mathematical Society, 2018. https://doi.org/10.1090/pspum/097.2/01700. ieee: T. D. Browning, “How often does the Hasse principle hold?,” presented at the Algebraic Geometry, Salt Lake City, Utah, USA, 2018, vol. 97, no. 2, pp. 89–102. ista: Browning TD. 2018. How often does the Hasse principle hold? Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, vol. 97, 89–102. mla: Browning, Timothy D. How Often Does the Hasse Principle Hold? Vol. 97, no. 2, American Mathematical Society, 2018, pp. 89–102, doi:10.1090/pspum/097.2/01700. short: T.D. Browning, in:, American Mathematical Society, 2018, pp. 89–102. conference: end_date: 2015-07-10 location: Salt Lake City, Utah, USA name: Algebraic Geometry start_date: 2015-07-06 date_created: 2018-12-11T11:45:01Z date_published: 2018-01-01T00:00:00Z date_updated: 2021-01-12T06:52:54Z day: '01' doi: 10.1090/pspum/097.2/01700 extern: '1' intvolume: ' 97' issue: '2' language: - iso: eng month: '01' oa_version: None page: 89 - 102 publication_status: published publisher: American Mathematical Society quality_controlled: '1' status: public title: How often does the Hasse principle hold? type: conference user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 97 year: '2018' ... --- _id: '176' abstract: - lang: eng text: For a general class of non-negative functions defined on integral ideals of number fields, upper bounds are established for their average over the values of certain principal ideals that are associated to irreducible binary forms with integer coefficients. article_processing_charge: No 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: Efthymios full_name: Sofos, Efthymios last_name: Sofos citation: ama: Browning TD, Sofos E. Averages of arithmetic functions over principal ideals. International Journal of Nuber Theory. 2018;15(3):547-567. doi:10.1142/S1793042119500283 apa: Browning, T. D., & Sofos, E. (2018). Averages of arithmetic functions over principal ideals. International Journal of Nuber Theory. World Scientific Publishing. https://doi.org/10.1142/S1793042119500283 chicago: Browning, Timothy D, and Efthymios Sofos. “Averages of Arithmetic Functions over Principal Ideals.” International Journal of Nuber Theory. World Scientific Publishing, 2018. https://doi.org/10.1142/S1793042119500283. ieee: T. D. Browning and E. Sofos, “Averages of arithmetic functions over principal ideals,” International Journal of Nuber Theory, vol. 15, no. 3. World Scientific Publishing, pp. 547–567, 2018. ista: Browning TD, Sofos E. 2018. Averages of arithmetic functions over principal ideals. International Journal of Nuber Theory. 15(3), 547–567. mla: Browning, Timothy D., and Efthymios Sofos. “Averages of Arithmetic Functions over Principal Ideals.” International Journal of Nuber Theory, vol. 15, no. 3, World Scientific Publishing, 2018, pp. 547–67, doi:10.1142/S1793042119500283. short: T.D. Browning, E. Sofos, International Journal of Nuber Theory 15 (2018) 547–567. date_created: 2018-12-11T11:45:01Z date_published: 2018-11-16T00:00:00Z date_updated: 2021-01-12T06:53:01Z day: '16' doi: 10.1142/S1793042119500283 extern: '1' external_id: arxiv: - '1706.04331' intvolume: ' 15' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1706.04331 month: '11' oa: 1 oa_version: Preprint page: 547-567 publication: International Journal of Nuber Theory publication_status: published publisher: World Scientific Publishing status: public title: Averages of arithmetic functions over principal ideals type: journal_article user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425 volume: 15 year: '2018' ... --- _id: '178' abstract: - lang: eng text: We give an upper bound for the number of rational points of height at most B, lying on a surface defined by a quadratic form Q. The bound shows an explicit dependence on Q. It is optimal with respect to B, and is also optimal for typical forms Q. article_processing_charge: No 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. Counting rational points on quadric surfaces. Discrete Analysis. 2018;15:1-29. doi:10.19086/da.4375 apa: Browning, T. D., & Heath-Brown, R. (2018). Counting rational points on quadric surfaces. Discrete Analysis. Alliance of Diamond Open Access Journals. https://doi.org/10.19086/da.4375 chicago: Browning, Timothy D, and Roger Heath-Brown. “Counting Rational Points on Quadric Surfaces.” Discrete Analysis. Alliance of Diamond Open Access Journals, 2018. https://doi.org/10.19086/da.4375. ieee: T. D. Browning and R. Heath-Brown, “Counting rational points on quadric surfaces,” Discrete Analysis, vol. 15. Alliance of Diamond Open Access Journals, pp. 1–29, 2018. ista: Browning TD, Heath-Brown R. 2018. Counting rational points on quadric surfaces. Discrete Analysis. 15, 1–29. mla: Browning, Timothy D., and Roger Heath-Brown. “Counting Rational Points on Quadric Surfaces.” Discrete Analysis, vol. 15, Alliance of Diamond Open Access Journals, 2018, pp. 1–29, doi:10.19086/da.4375. short: T.D. Browning, R. Heath-Brown, Discrete Analysis 15 (2018) 1–29. date_created: 2018-12-11T11:45:02Z date_published: 2018-09-07T00:00:00Z date_updated: 2022-08-26T09:13:02Z day: '07' ddc: - '512' doi: 10.19086/da.4375 extern: '1' external_id: arxiv: - '1801.00979' intvolume: ' 15' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1801.00979 month: '09' oa: 1 oa_version: Preprint page: 1 - 29 publication: Discrete Analysis publication_identifier: eissn: - 2397-3129 publication_status: published publisher: Alliance of Diamond Open Access Journals quality_controlled: '1' status: public title: Counting rational points on quadric 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2018' ... --- _id: '169' abstract: - lang: eng text: We show that a twisted variant of Linnik’s conjecture on sums of Kloosterman sums leads to an optimal covering exponent for S3. article_processing_charge: No 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: Vinay full_name: Kumaraswamy, Vinay last_name: Kumaraswamy - first_name: Rapael full_name: Steiner, Rapael last_name: Steiner citation: ama: Browning TD, Kumaraswamy V, Steiner R. Twisted Linnik implies optimal covering exponent for S3. International Mathematics Research Notices. 2017. doi:10.1093/imrn/rnx116 apa: Browning, T. D., Kumaraswamy, V., & Steiner, R. (2017). Twisted Linnik implies optimal covering exponent for S3. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnx116 chicago: Browning, Timothy D, Vinay Kumaraswamy, and Rapael Steiner. “Twisted Linnik Implies Optimal Covering Exponent for S3.” International Mathematics Research Notices. Oxford University Press, 2017. https://doi.org/10.1093/imrn/rnx116. ieee: T. D. Browning, V. Kumaraswamy, and R. Steiner, “Twisted Linnik implies optimal covering exponent for S3,” International Mathematics Research Notices. Oxford University Press, 2017. ista: Browning TD, Kumaraswamy V, Steiner R. 2017. Twisted Linnik implies optimal covering exponent for S3. International Mathematics Research Notices. mla: Browning, Timothy D., et al. “Twisted Linnik Implies Optimal Covering Exponent for S3.” International Mathematics Research Notices, Oxford University Press, 2017, doi:10.1093/imrn/rnx116. short: T.D. Browning, V. Kumaraswamy, R. Steiner, International Mathematics Research Notices (2017). date_created: 2018-12-11T11:44:59Z date_published: 2017-06-19T00:00:00Z date_updated: 2021-01-12T06:52:32Z day: '19' doi: 10.1093/imrn/rnx116 extern: '1' external_id: arxiv: - '1609.06097' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1609.06097 month: '06' oa: 1 oa_version: None publication: International Mathematics Research Notices publication_status: published publisher: Oxford University Press publist_id: '7752' quality_controlled: '1' status: public title: Twisted Linnik implies optimal covering exponent for S3 type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2017' ... --- _id: '172' abstract: - lang: eng text: We study strong approximation for some algebraic varieties over ℚ which are defined using norm forms. This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg. article_processing_charge: No 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: Damaris full_name: Schindler, Damaris last_name: Schindler citation: ama: Browning TD, Schindler D. Strong approximation and a conjecture of Harpaz and Wittenberg. International Mathematics Research Notices. 2017. doi:10.1093/imrn/rnx252 apa: Browning, T. D., & Schindler, D. (2017). Strong approximation and a conjecture of Harpaz and Wittenberg. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnx252 chicago: Browning, Timothy D, and Damaris Schindler. “Strong Approximation and a Conjecture of Harpaz and Wittenberg.” International Mathematics Research Notices. Oxford University Press, 2017. https://doi.org/10.1093/imrn/rnx252. ieee: T. D. Browning and D. Schindler, “Strong approximation and a conjecture of Harpaz and Wittenberg,” International Mathematics Research Notices. Oxford University Press, 2017. ista: Browning TD, Schindler D. 2017. Strong approximation and a conjecture of Harpaz and Wittenberg. International Mathematics Research Notices. mla: Browning, Timothy D., and Damaris Schindler. “Strong Approximation and a Conjecture of Harpaz and Wittenberg.” International Mathematics Research Notices, Oxford University Press, 2017, doi:10.1093/imrn/rnx252. short: T.D. Browning, D. Schindler, International Mathematics Research Notices (2017). date_created: 2018-12-11T11:45:00Z date_published: 2017-10-30T00:00:00Z date_updated: 2021-01-12T06:52:45Z day: '30' doi: 10.1093/imrn/rnx252 extern: '1' external_id: arxiv: - '1509.07744' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1509.07744 month: '10' oa: 1 oa_version: None publication: International Mathematics Research Notices publication_status: published publisher: Oxford University Press publist_id: '7749' quality_controlled: '1' status: public title: Strong approximation and a conjecture of Harpaz and Wittenberg type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2017' ...