[{"day":"26","article_processing_charge":"No","scopus_import":"1","date_published":"2023-05-26T00:00:00Z","publication":"Involve","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","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.","short":"T.D. Browning, J. Lyczak, R. Sarapin, Involve 16 (2023) 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.","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."},"article_type":"original","page":"331-342","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"}],"issue":"2","type":"journal_article","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13180","title":"Local solubility for a family of quadrics over a split quadric surface","status":"public","intvolume":" 16","month":"05","publication_identifier":{"eissn":["1944-4184"],"issn":["1944-4176"]},"doi":"10.2140/involve.2023.16.331","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2203.06881","open_access":"1"}],"external_id":{"arxiv":["2203.06881"]},"quality_controlled":"1","author":[{"last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D"},{"id":"3572849A-F248-11E8-B48F-1D18A9856A87","first_name":"Julian","last_name":"Lyczak","full_name":"Lyczak, Julian"},{"full_name":"Sarapin, Roman","last_name":"Sarapin","first_name":"Roman"}],"date_updated":"2023-07-17T08:39:19Z","date_created":"2023-07-02T22:00:43Z","volume":16,"year":"2023","publication_status":"published","department":[{"_id":"TiBr"}],"publisher":"Mathematical Sciences Publishers"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"13091","ddc":["510"],"title":"Free rational curves on low degree hypersurfaces and the circle method","status":"public","intvolume":" 17","oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":1430719,"creator":"dernst","access_level":"open_access","file_name":"2023_AlgebraNumberTheory_Browning.pdf","checksum":"5d5d67b235905650e33cf7065d7583b4","success":1,"date_updated":"2023-05-30T08:05:22Z","date_created":"2023-05-30T08:05:22Z","relation":"main_file","file_id":"13101"}],"type":"journal_article","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."}],"issue":"3","publication":"Algebra and Number Theory","citation":{"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","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.","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","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.","short":"T.D. Browning, W. Sawin, Algebra and Number Theory 17 (2023) 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."},"article_type":"original","page":"719-748","date_published":"2023-04-12T00:00:00Z","scopus_import":"1","day":"12","article_processing_charge":"No","has_accepted_license":"1","year":"2023","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.","publication_status":"published","department":[{"_id":"TiBr"}],"publisher":"Mathematical Sciences Publishers","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Sawin, Will","last_name":"Sawin","first_name":"Will"}],"date_updated":"2023-08-01T14:51:57Z","date_created":"2023-05-28T22:01:02Z","volume":17,"file_date_updated":"2023-05-30T08:05:22Z","external_id":{"arxiv":["1810.06882"],"isi":["000996014700004"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425","name":"Between rational and integral points"}],"doi":"10.2140/ant.2023.17.719","language":[{"iso":"eng"}],"month":"04","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]}},{"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8682","status":"public","title":"The Hasse principle for random Fano hypersurfaces","intvolume":" 197","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."}],"issue":"3","type":"journal_article","date_published":"2023-05-01T00:00:00Z","publication":"Annals of Mathematics","citation":{"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.","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.","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","ista":"Browning TD, Boudec PL, Sawin W. 2023. The Hasse principle for random Fano hypersurfaces. Annals of Mathematics. 197(3), 1115–1203.","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","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."},"article_type":"original","page":"1115-1203","day":"01","article_processing_charge":"No","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Boudec, Pierre Le","last_name":"Boudec","first_name":"Pierre Le"},{"full_name":"Sawin, Will","first_name":"Will","last_name":"Sawin"}],"related_material":{"link":[{"description":"News on IST Homepage","relation":"press_release","url":"https://ist.ac.at/en/news/when-is-necessary-sufficient/"}]},"date_created":"2020-10-19T14:28:50Z","date_updated":"2023-10-17T12:47:43Z","volume":197,"year":"2023","publication_status":"published","department":[{"_id":"TiBr"}],"publisher":"Princeton University","doi":"10.4007/annals.2023.197.3.3","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2006.02356"}],"oa":1,"external_id":{"isi":["000966611000003"],"arxiv":["2006.02356"]},"isi":1,"quality_controlled":"1","month":"05","publication_identifier":{"issn":["0003-486X"]}},{"volume":24,"date_created":"2023-05-07T22:01:04Z","date_updated":"2023-10-18T06:54:30Z","author":[{"first_name":"Dante","last_name":"Bonolis","id":"6A459894-5FDD-11E9-AF35-BB24E6697425","full_name":"Bonolis, Dante"},{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D"}],"publisher":"Scuola Normale Superiore - Edizioni della Normale","department":[{"_id":"TiBr"}],"publication_status":"published","year":"2023","publication_identifier":{"issn":["0391-173X"],"eissn":["2036-2145"]},"month":"02","language":[{"iso":"eng"}],"doi":"10.2422/2036-2145.202010_018","quality_controlled":"1","external_id":{"arxiv":["2007.14182"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2007.14182"}],"issue":"1","abstract":[{"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","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","intvolume":" 24","title":"Uniform bounds for rational points on hyperelliptic fibrations","status":"public","_id":"12916","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","day":"16","scopus_import":"1","date_published":"2023-02-16T00:00:00Z","page":"173-204","article_type":"original","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","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.","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.","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","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.","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."},"publication":"Annali della Scuola Normale Superiore di Pisa - Classe di Scienze"},{"oa_version":"Preprint","title":"Equidistribution and freeness on Grassmannians","status":"public","intvolume":" 16","_id":"9199","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"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.","lang":"eng"}],"issue":"10","type":"journal_article","date_published":"2022-12-01T00:00:00Z","article_type":"original","page":"2385-2407","publication":"Algebra & Number Theory","citation":{"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.","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.","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","ista":"Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians. Algebra & Number Theory. 16(10), 2385–2407.","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","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."},"day":"01","article_processing_charge":"No","scopus_import":"1","date_created":"2021-02-25T09:56:57Z","date_updated":"2023-08-02T06:46:38Z","volume":16,"author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D"},{"id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","last_name":"Horesh","first_name":"Tal","full_name":"Horesh, Tal"},{"orcid":"0000-0001-7302-8256","id":"560601DA-8D36-11E9-A136-7AC1E5697425","last_name":"Wilsch","first_name":"Florian Alexander","full_name":"Wilsch, Florian Alexander"}],"publication_status":"published","publisher":"Mathematical Sciences Publishers","department":[{"_id":"TiBr"}],"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.","year":"2022","language":[{"iso":"eng"}],"doi":"10.2140/ant.2022.16.2385","quality_controlled":"1","isi":1,"project":[{"name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2"},{"call_identifier":"FWF","name":"New frontiers of the Manin conjecture","grant_number":"P32428","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425"}],"oa":1,"external_id":{"isi":["000961514100004"],"arxiv":["2102.11552"]},"main_file_link":[{"url":"https://arxiv.org/abs/2102.11552","open_access":"1"}],"month":"12","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]}},{"department":[{"_id":"TiBr"}],"publisher":"State University of New York","publication_status":"published","year":"2022","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.","volume":28,"date_created":"2023-03-28T09:21:09Z","date_updated":"2023-10-18T07:59:13Z","author":[{"full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D"}],"file_date_updated":"2023-03-30T07:09:35Z","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","call_identifier":"FWF","name":"New frontiers of the Manin conjecture"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1076-9803"]},"month":"08","intvolume":" 28","ddc":["510"],"status":"public","title":"Revisiting the Manin–Peyre conjecture for the split del Pezzo surface of degree 5","_id":"12776","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"12778","checksum":"c01e8291794a1bdb7416aa103cb68ef8","success":1,"date_updated":"2023-03-30T07:09:35Z","date_created":"2023-03-30T07:09:35Z","access_level":"open_access","file_name":"2022_NYJM_Browning.pdf","file_size":897267,"content_type":"application/pdf","creator":"dernst"}],"type":"journal_article","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."}],"page":"1193 - 1229","article_type":"original","citation":{"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.","short":"T.D. Browning, New York Journal of Mathematics 28 (2022) 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.","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.","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.","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.","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."},"publication":"New York Journal of Mathematics","date_published":"2022-08-24T00:00:00Z","has_accepted_license":"1","article_processing_charge":"No","day":"24"},{"scopus_import":"1","publication_identifier":{"eissn":["2296-505X"],"isbn":["978-3-030-86871-0"],"eisbn":["978-3-030-86872-7"],"issn":["0743-1643"]},"article_processing_charge":"No","month":"12","day":"01","page":"XIV, 166","quality_controlled":"1","citation":{"ista":"Browning TD. 2021. Cubic Forms and the Circle Method, Cham: Springer Nature, XIV, 166p.","ieee":"T. D. Browning, Cubic Forms and the Circle Method, vol. 343. Cham: Springer Nature, 2021.","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","ama":"Browning TD. Cubic Forms and the Circle Method. Vol 343. Cham: Springer Nature; 2021. doi: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.","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."},"language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-86872-7","date_published":"2021-12-01T00:00:00Z","place":"Cham","alternative_title":["Progress in Mathematics"],"type":"book","abstract":[{"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.","lang":"eng"}],"publisher":"Springer Nature","department":[{"_id":"TiBr"}],"intvolume":" 343","title":"Cubic Forms and the Circle Method","publication_status":"published","status":"public","year":"2021","_id":"10415","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":343,"oa_version":"None","date_updated":"2022-06-03T07:38:33Z","date_created":"2021-12-05T23:01:46Z","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning"}]},{"scopus_import":"1","day":"05","has_accepted_license":"1","article_processing_charge":"No","publication":"Mathematische Zeitschrift","citation":{"short":"T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 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.","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.","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","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."},"article_type":"original","page":"1071–1101","date_published":"2021-03-05T00:00:00Z","type":"journal_article","abstract":[{"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.","lang":"eng"}],"_id":"9260","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"title":"Arithmetic of higher-dimensional orbifolds and a mixed Waring problem","status":"public","intvolume":" 299","oa_version":"Published Version","file":[{"success":1,"checksum":"8ed9f49568806894744096dbbca0ad7b","date_updated":"2021-03-22T12:41:26Z","date_created":"2021-03-22T12:41:26Z","file_id":"9279","relation":"main_file","creator":"dernst","file_size":492685,"content_type":"application/pdf","access_level":"open_access","file_name":"2021_MathZeitschrift_Browning.pdf"}],"month":"03","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"external_id":{"isi":["000625573800002"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","isi":1,"project":[{"name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2"}],"doi":"10.1007/s00209-021-02695-w","language":[{"iso":"eng"}],"file_date_updated":"2021-03-22T12:41:26Z","year":"2021","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.","publication_status":"published","department":[{"_id":"TiBr"}],"publisher":"Springer Nature","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning"},{"last_name":"Yamagishi","first_name":"Shuntaro","full_name":"Yamagishi, Shuntaro"}],"date_created":"2021-03-21T23:01:21Z","date_updated":"2023-08-07T14:20:00Z","volume":299},{"type":"journal_article","issue":"1","abstract":[{"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.","lang":"eng"}],"intvolume":" 33","status":"public","title":"The geometric sieve for quadrics","_id":"8742","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","page":"147-165","article_type":"original","citation":{"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.","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","ista":"Browning TD, Heath-Brown R. 2021. The geometric sieve for quadrics. Forum Mathematicum. 33(1), 147–165.","ama":"Browning TD, Heath-Brown R. 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Commentarii Mathematici Helvetici. 2020;95(4):635-659. doi:10.4171/CMH/499"},"article_type":"original","page":"635-659","date_published":"2020-12-07T00:00:00Z","type":"journal_article","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."}],"issue":"4","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9007","title":"Free rational points on smooth hypersurfaces","status":"public","intvolume":" 95","oa_version":"Preprint"},{"publication_status":"published","department":[{"_id":"TiBr"}],"publisher":"Duke University Press","year":"2020","date_created":"2018-12-11T11:45:02Z","date_updated":"2023-10-17T12:51:10Z","volume":169,"author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning"},{"first_name":"Roger","last_name":"Heath Brown","full_name":"Heath Brown, Roger"}],"isi":1,"quality_controlled":"1","oa":1,"external_id":{"isi":["000582676300002"],"arxiv":["1805.10715"]},"main_file_link":[{"url":"https://arxiv.org/abs/1805.10715","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1215/00127094-2020-0031","month":"09","publication_identifier":{"issn":["0012-7094"]},"title":"Density of rational points on a quadric bundle in ℙ3×ℙ3","status":"public","intvolume":" 169","_id":"179","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"journal_article","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."}],"issue":"16","article_type":"original","page":"3099-3165","publication":"Duke Mathematical Journal","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","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.","short":"T.D. Browning, R. Heath Brown, Duke Mathematical Journal 169 (2020) 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.","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."},"date_published":"2020-09-10T00:00:00Z","day":"10","article_processing_charge":"No"},{"date_published":"2019-04-01T00:00:00Z","page":"977-1016","citation":{"short":"T.D. Browning, E. Sofos, Mathematische Annalen 373 (2019) 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.","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.","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","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.","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","ista":"Browning TD, Sofos E. 2019. Counting rational points on quartic del Pezzo surfaces with a rational conic. 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American Mathematical Society, 2019. https://doi.org/10.1090/tran/7514.","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.","ista":"Browning TD, Loughran D. 2019. Sieving rational points on varieties. Transactions of the American Mathematical Society. 371(8), 5757–5785.","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.","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","ama":"Browning TD, Loughran D. 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In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.","lang":"eng"}]},{"external_id":{"arxiv":["1810.08426"],"isi":["000468857300025"]},"oa":1,"quality_controlled":"1","isi":1,"doi":"10.1016/j.aim.2019.04.031","language":[{"iso":"eng"}],"month":"06","publication_identifier":{"issn":["00018708"],"eissn":["10902082"]},"year":"2019","publication_status":"published","department":[{"_id":"TiBr"}],"publisher":"Elsevier","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D"},{"first_name":"L.Q.","last_name":"Hu","full_name":"Hu, L.Q."}],"date_updated":"2023-08-25T10:11:55Z","date_created":"2019-04-16T09:13:25Z","volume":349,"file_date_updated":"2020-07-14T12:47:27Z","publication":"Advances in Mathematics","citation":{"ieee":"T. D. Browning and L. Q. Hu, “Counting rational points on biquadratic hypersurfaces,” Advances in Mathematics, vol. 349. Elsevier, pp. 920–940, 2019.","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","ista":"Browning TD, Hu LQ. 2019. Counting rational points on biquadratic hypersurfaces. Advances in Mathematics. 349, 920–940.","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","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.","short":"T.D. Browning, L.Q. Hu, Advances in Mathematics 349 (2019) 920–940.","mla":"Browning, Timothy D., and L. Q. 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The proof uses the Hardy–Littlewood circle method."}]},{"article_processing_charge":"No","month":"01","day":"01","doi":"10.1090/pspum/097.2/01700","date_published":"2018-01-01T00:00:00Z","conference":{"end_date":"2015-07-10","location":"Salt Lake City, Utah, USA","start_date":"2015-07-06","name":"Algebraic Geometry"},"language":[{"iso":"eng"}],"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","ista":"Browning TD. 2018. How often does the Hasse principle hold? Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, vol. 97, 89–102.","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","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.","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.","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."},"page":"89 - 102","quality_controlled":"1","issue":"2","abstract":[{"lang":"eng","text":"We survey recent efforts to quantify failures of the Hasse principle in families of rationally connected varieties."}],"extern":"1","type":"conference","alternative_title":["Proceedings of Symposia in Pure Mathematics"],"author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D"}],"volume":97,"oa_version":"None","date_created":"2018-12-11T11:45:01Z","date_updated":"2021-01-12T06:52:54Z","_id":"174","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","year":"2018","intvolume":" 97","publisher":"American Mathematical Society","title":"How often does the Hasse principle hold?","status":"public","publication_status":"published"},{"_id":"176","year":"2018","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","intvolume":" 15","publisher":"World Scientific Publishing","title":"Averages of arithmetic functions over principal ideals","status":"public","publication_status":"published","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D"},{"first_name":"Efthymios","last_name":"Sofos","full_name":"Sofos, Efthymios"}],"volume":15,"oa_version":"Preprint","date_created":"2018-12-11T11:45:01Z","date_updated":"2021-01-12T06:53:01Z","type":"journal_article","issue":"3","abstract":[{"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.","lang":"eng"}],"extern":"1","oa":1,"citation":{"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.","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.","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","ista":"Browning TD, Sofos E. 2018. Averages of arithmetic functions over principal ideals. International Journal of Nuber Theory. 15(3), 547–567.","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","ieee":"T. D. Browning and E. Sofos, “Averages of arithmetic functions over principal ideals,” International Journal of Nuber Theory, vol. 15, no. 3. 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It is optimal with respect to B, and is also optimal for typical forms Q."}],"type":"journal_article","doi":"10.19086/da.4375","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1801.00979"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1801.00979"}],"quality_controlled":"1","publication_identifier":{"eissn":["2397-3129"]},"month":"09","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D"},{"last_name":"Heath-Brown","first_name":"Roger","full_name":"Heath-Brown, Roger"}],"volume":15,"date_updated":"2022-08-26T09:13:02Z","date_created":"2018-12-11T11:45:02Z","year":"2018","publisher":"Alliance of Diamond Open Access Journals","publication_status":"published","extern":"1"},{"type":"journal_article","extern":"1","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."}],"publist_id":"7752","status":"public","title":"Twisted Linnik implies optimal covering exponent for S3","publication_status":"published","publisher":"Oxford University Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"169","year":"2017","date_created":"2018-12-11T11:44:59Z","date_updated":"2021-01-12T06:52:32Z","oa_version":"None","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Kumaraswamy, Vinay","first_name":"Vinay","last_name":"Kumaraswamy"},{"first_name":"Rapael","last_name":"Steiner","full_name":"Steiner, Rapael"}],"month":"06","day":"19","article_processing_charge":"No","quality_controlled":"1","publication":"International Mathematics Research Notices","citation":{"chicago":"Browning, Timothy D, Vinay Kumaraswamy, and Rapael Steiner. “Twisted Linnik Implies Optimal Covering Exponent for S3.” International Mathematics Research Notices. 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This allows us to confirm a special case of a conjecture due to Harpaz and Wittenberg."}],"publist_id":"7749","extern":"1","type":"journal_article","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schindler, Damaris","first_name":"Damaris","last_name":"Schindler"}],"date_created":"2018-12-11T11:45:00Z","date_updated":"2021-01-12T06:52:45Z","oa_version":"None","_id":"172","year":"2017","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_status":"published","title":"Strong approximation and a conjecture of Harpaz and Wittenberg","publisher":"Oxford University Press","day":"30","month":"10","article_processing_charge":"No","doi":"10.1093/imrn/rnx252","date_published":"2017-10-30T00:00:00Z","language":[{"iso":"eng"}],"publication":"International Mathematics Research Notices","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1509.07744"}],"oa":1,"citation":{"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).","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.","ama":"Browning TD, Schindler D. Strong approximation and a conjecture of Harpaz and Wittenberg. International Mathematics Research Notices. 2017. doi:10.1093/imrn/rnx252","ista":"Browning TD, Schindler D. 2017. Strong approximation and a conjecture of Harpaz and Wittenberg. International Mathematics Research Notices.","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","ieee":"T. D. Browning and D. Schindler, “Strong approximation and a conjecture of Harpaz and Wittenberg,” International Mathematics Research Notices. 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