[{"doi":"10.2140/ant.2023.17.719","arxiv":1,"researchdata_availability":"no","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425","name":"Between rational and integral points"}],"publisher":"Mathematical Sciences Publishers","publication_status":"published","intvolume":"        17","date_published":"2023-04-12T00:00:00Z","date_updated":"2026-07-29T10:11:06Z","oa":1,"status":"public","month":"04","title":"Free rational curves on low degree hypersurfaces and the circle method","scopus_import":"1","author":[{"last_name":"Browning","full_name":"Browning, Timothy D","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"first_name":"Will","full_name":"Sawin, Will","last_name":"Sawin"}],"issue":"3","file_date_updated":"2023-05-30T08:05:22Z","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","ddc":["510"],"article_type":"original","publication":"Algebra & Number Theory","year":"2023","das_tickbox":"0","isi":1,"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.","supplementarymaterial":"no","department":[{"_id":"TiBr"}],"type":"journal_article","article_processing_charge":"No","volume":17,"page":"719-748","citation":{"ama":"Browning TD, Sawin W. Free rational curves on low degree hypersurfaces and the circle method. <i>Algebra &#38; Number Theory</i>. 2023;17(3):719-748. doi:<a href=\"https://doi.org/10.2140/ant.2023.17.719\">10.2140/ant.2023.17.719</a>","apa":"Browning, T. D., &#38; Sawin, W. (2023). Free rational curves on low degree hypersurfaces and the circle method. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2023.17.719\">https://doi.org/10.2140/ant.2023.17.719</a>","chicago":"Browning, Timothy D, and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2023. <a href=\"https://doi.org/10.2140/ant.2023.17.719\">https://doi.org/10.2140/ant.2023.17.719</a>.","mla":"Browning, Timothy D., and Will Sawin. “Free Rational Curves on Low Degree Hypersurfaces and the Circle Method.” <i>Algebra &#38; Number Theory</i>, vol. 17, no. 3, Mathematical Sciences Publishers, 2023, pp. 719–48, doi:<a href=\"https://doi.org/10.2140/ant.2023.17.719\">10.2140/ant.2023.17.719</a>.","ista":"Browning TD, Sawin W. 2023. Free rational curves on low degree hypersurfaces and the circle method. Algebra &#38; Number Theory. 17(3), 719–748.","short":"T.D. Browning, W. Sawin, Algebra &#38; Number Theory 17 (2023) 719–748.","ieee":"T. D. Browning and W. Sawin, “Free rational curves on low degree hypersurfaces and the circle method,” <i>Algebra &#38; Number Theory</i>, vol. 17, no. 3. Mathematical Sciences Publishers, pp. 719–748, 2023."},"date_created":"2023-05-28T22:01:02Z","corr_author":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"relation":"main_file","creator":"dernst","file_name":"2023_AlgebraNumberTheory_Browning.pdf","access_level":"open_access","date_updated":"2023-05-30T08:05:22Z","content_type":"application/pdf","date_created":"2023-05-30T08:05:22Z","file_size":1430719,"file_id":"13101","checksum":"5d5d67b235905650e33cf7065d7583b4","success":1}],"external_id":{"arxiv":["1810.06882"],"isi":["000996014700004"]},"fulldoi":"https://doi.org/10.2140/ant.2023.17.719","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"_id":"13091","day":"12","license":"https://creativecommons.org/licenses/by/4.0/","has_accepted_license":"1"},{"volume":74,"page":"1253-1294","citation":{"short":"T. Horesh, Y. Karasik, Quarterly Journal of Mathematics 74 (2023) 1253–1294.","ieee":"T. Horesh and Y. Karasik, “Equidistribution of primitive lattices in ℝn,” <i>Quarterly Journal of Mathematics</i>, vol. 74, no. 4. Oxford University Press, pp. 1253–1294, 2023.","ista":"Horesh T, Karasik Y. 2023. Equidistribution of primitive lattices in ℝn. Quarterly Journal of Mathematics. 74(4), 1253–1294.","apa":"Horesh, T., &#38; Karasik, Y. (2023). Equidistribution of primitive lattices in ℝn. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haad008\">https://doi.org/10.1093/qmath/haad008</a>","chicago":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2023. <a href=\"https://doi.org/10.1093/qmath/haad008\">https://doi.org/10.1093/qmath/haad008</a>.","ama":"Horesh T, Karasik Y. Equidistribution of primitive lattices in ℝn. <i>Quarterly Journal of Mathematics</i>. 2023;74(4):1253-1294. doi:<a href=\"https://doi.org/10.1093/qmath/haad008\">10.1093/qmath/haad008</a>","mla":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” <i>Quarterly Journal of Mathematics</i>, vol. 74, no. 4, Oxford University Press, 2023, pp. 1253–94, doi:<a href=\"https://doi.org/10.1093/qmath/haad008\">10.1093/qmath/haad008</a>."},"date_created":"2023-12-31T23:01:03Z","corr_author":"1","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"acknowledgement":"This work was done when both authors were visiting Institute of Science and Technology (IST) Austria. T.H. was being supported by Engineering and Physical Sciences Research Council grant EP/P026710/1. Y.K. had a great time there and is grateful for the hospitality. The appendix to this paper is largely based on a mini course T.H. had given at IST in February 2020.","supplementarymaterial":"no","department":[{"_id":"TiBr"}],"type":"journal_article","article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"_id":"14717","has_accepted_license":"1","day":"01","file":[{"checksum":"bf29baa9eae8500f3374dbcb80712687","success":1,"content_type":"application/pdf","date_created":"2024-01-02T07:37:09Z","file_size":724748,"file_id":"14720","date_updated":"2024-01-02T07:37:09Z","creator":"dernst","relation":"main_file","file_name":"2023_QuarterlyJourMath_Horesh.pdf","access_level":"open_access"}],"external_id":{"arxiv":["2012.04508"],"isi":["001005945400001"]},"fulldoi":"https://doi.org/10.1093/qmath/haad008","publication_status":"published","intvolume":"        74","date_published":"2023-12-01T00:00:00Z","doi":"10.1093/qmath/haad008","researchdata_availability":"no","arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"name":"Between rational and integral points","grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425"}],"publisher":"Oxford University Press","abstract":[{"text":"We count primitive lattices of rank d inside Zn as their covolume tends to infinity, with respect to certain parameters of such lattices. These parameters include, for example, the subspace that a lattice spans, namely its projection to the Grassmannian; its homothety class and its equivalence class modulo rescaling and rotation, often referred to as a shape. We add to a prior work of Schmidt by allowing sets in the spaces of parameters that are general enough to conclude the joint equidistribution of these parameters. In addition to the primitive d-lattices Λ themselves, we also consider their orthogonal complements in Zn⁠, A1⁠, and show that the equidistribution occurs jointly for Λ and A1⁠. Finally, our asymptotic formulas for the number of primitive lattices include an explicit bound on the error term.","lang":"eng"}],"oa_version":"Published Version","article_type":"original","ddc":["510"],"publication":"Quarterly Journal of Mathematics","year":"2023","das_tickbox":"0","isi":1,"date_updated":"2026-07-29T10:22:09Z","oa":1,"status":"public","title":"Equidistribution of primitive lattices in ℝn","month":"12","scopus_import":"1","issue":"4","author":[{"id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal","last_name":"Horesh","full_name":"Horesh, Tal"},{"first_name":"Yakov","full_name":"Karasik, Yakov","last_name":"Karasik"}],"file_date_updated":"2024-01-02T07:37:09Z"},{"arxiv":1,"researchdata_availability":"no","doi":"10.5802/pmb.50","publisher":"Presses Universitaires de Franche-Comté","project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2","name":"Between rational and integral points"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2023-06-15T00:00:00Z","intvolume":"      2023","publication_status":"published","author":[{"first_name":"Antonin","full_name":"Guilloux, Antonin","last_name":"Guilloux"},{"full_name":"Horesh, Tal","last_name":"Horesh","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal"}],"title":"p-adic directions of primitive vectors","scopus_import":"1","month":"06","oa":1,"status":"public","date_updated":"2026-07-29T10:40:38Z","file_date_updated":"2024-10-07T11:32:32Z","ddc":["510"],"article_type":"original","oa_version":"Published Version","abstract":[{"text":"Linnik type problems concern the distribution of projections of integral points on the unit sphere as their norm increases, and different generalizations of this phenomenon. Our work addresses a question of this type: we prove the uniform distribution of the projections of primitive Z2 points in the p-adic unit sphere, as their (real) norm tends to infinity. The proof is via counting lattice points in semi-simple S-arithmetic groups.","lang":"eng"},{"lang":"fre","text":"Les problèmes de type Linnik concernent la distribution des projections des points entiers sur la sphère unitaire lorsque leur norme augmente et différentes généralisations de ce phénomène. Notre travail s’intéresse à une question de ce type : nous prouvons la distribution uniforme des projections des points primitifs de Z2 sur la sphère unitaire p-adique lorsque leur norme (réelle) tend vers l’infini. La preuve se fait en comptant les points d’un réseau dans des S-groupes arithmétiques semi-simples."}],"das_tickbox":"0","year":"2023","publication":"Publications mathématiques de Besançon - Algèbre et Théorie des nombres","supplementarymaterial":"no","acknowledgement":"The second author is supported by EPRSC grant EP/P026710/1.","type":"journal_article","article_processing_charge":"Yes (in subscription journal)","department":[{"_id":"TiBr"}],"page":"85-107","volume":2023,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)"},"corr_author":"1","date_created":"2024-10-06T22:01:13Z","citation":{"mla":"Guilloux, Antonin, and Tal Horesh. “P-Adic Directions of Primitive Vectors.” <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>, vol. 2023, Presses Universitaires de Franche-Comté, 2023, pp. 85–107, doi:<a href=\"https://doi.org/10.5802/pmb.50\">10.5802/pmb.50</a>.","chicago":"Guilloux, Antonin, and Tal Horesh. “P-Adic Directions of Primitive Vectors.” <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>. Presses Universitaires de Franche-Comté, 2023. <a href=\"https://doi.org/10.5802/pmb.50\">https://doi.org/10.5802/pmb.50</a>.","apa":"Guilloux, A., &#38; Horesh, T. (2023). p-adic directions of primitive vectors. <i>Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres</i>. Presses Universitaires de Franche-Comté. <a href=\"https://doi.org/10.5802/pmb.50\">https://doi.org/10.5802/pmb.50</a>","ama":"Guilloux A, Horesh T. p-adic directions of primitive vectors. <i>Publications mathématiques de Besançon - Algèbre et Théorie des nombres</i>. 2023;2023:85-107. doi:<a href=\"https://doi.org/10.5802/pmb.50\">10.5802/pmb.50</a>","ista":"Guilloux A, Horesh T. 2023. p-adic directions of primitive vectors. Publications mathématiques de Besançon - Algèbre et Théorie des nombres. 2023, 85–107.","ieee":"A. Guilloux and T. Horesh, “p-adic directions of primitive vectors,” <i>Publications mathématiques de Besançon - Algèbre et Théorie des nombres</i>, vol. 2023. Presses Universitaires de Franche-Comté, pp. 85–107, 2023.","short":"A. Guilloux, T. Horesh, Publications Mathématiques de Besançon - Algèbre et Théorie Des Nombres 2023 (2023) 85–107."},"external_id":{"arxiv":["2103.10889"]},"file":[{"date_created":"2024-10-07T11:32:32Z","content_type":"application/pdf","file_id":"18186","file_size":1399390,"checksum":"cefc47a2cf55a87f8e4960197f73353b","success":1,"file_name":"2023_MathBesancon_Guilloux.pdf","creator":"dernst","relation":"main_file","access_level":"open_access","date_updated":"2024-10-07T11:32:32Z"}],"fulldoi":"https://doi.org/10.5802/pmb.50","language":[{"iso":"eng"}],"quality_controlled":"1","has_accepted_license":"1","license":"https://creativecommons.org/licenses/by-nd/4.0/","day":"15","_id":"18179","publication_identifier":{"eissn":["2592-6616"],"issn":["2804-8504"]}},{"supplementarymaterial":"no","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.","department":[{"_id":"TiBr"}],"type":"journal_article","article_processing_charge":"No","page":"2385-2407","volume":16,"corr_author":"1","citation":{"ieee":"T. D. Browning, T. Horesh, and F. A. Wilsch, “Equidistribution and freeness on Grassmannians,” <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10. Mathematical Sciences Publishers, pp. 2385–2407, 2022.","short":"T.D. Browning, T. Horesh, F.A. Wilsch, Algebra &#38; Number Theory 16 (2022) 2385–2407.","ista":"Browning TD, Horesh T, Wilsch FA. 2022. Equidistribution and freeness on Grassmannians. Algebra &#38; Number Theory. 16(10), 2385–2407.","mla":"Browning, Timothy D., et al. “Equidistribution and Freeness on Grassmannians.” <i>Algebra &#38; Number Theory</i>, vol. 16, no. 10, Mathematical Sciences Publishers, 2022, pp. 2385–407, doi:<a href=\"https://doi.org/10.2140/ant.2022.16.2385\">10.2140/ant.2022.16.2385</a>.","apa":"Browning, T. D., Horesh, T., &#38; Wilsch, F. A. (2022). Equidistribution and freeness on Grassmannians. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2022.16.2385\">https://doi.org/10.2140/ant.2022.16.2385</a>","chicago":"Browning, Timothy D, Tal Horesh, and Florian Alexander Wilsch. “Equidistribution and Freeness on Grassmannians.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2022. <a href=\"https://doi.org/10.2140/ant.2022.16.2385\">https://doi.org/10.2140/ant.2022.16.2385</a>.","ama":"Browning TD, Horesh T, Wilsch FA. Equidistribution and freeness on Grassmannians. <i>Algebra &#38; Number Theory</i>. 2022;16(10):2385-2407. doi:<a href=\"https://doi.org/10.2140/ant.2022.16.2385\">10.2140/ant.2022.16.2385</a>"},"date_created":"2021-02-25T09:56:57Z","external_id":{"arxiv":["2102.11552"],"isi":["000961514100004"]},"fulldoi":"https://doi.org/10.2140/ant.2022.16.2385","quality_controlled":"1","language":[{"iso":"eng"}],"day":"01","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"_id":"9199","arxiv":1,"researchdata_availability":"no","doi":"10.2140/ant.2022.16.2385","project":[{"name":"Between rational and integral points","grant_number":"EP-P026710-2","_id":"26A8D266-B435-11E9-9278-68D0E5697425"},{"name":"New frontiers of the Manin conjecture","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","call_identifier":"FWF"}],"publisher":"Mathematical Sciences Publishers","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2022-12-01T00:00:00Z","intvolume":"        16","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/2102.11552","open_access":"1"}],"scopus_import":"1","month":"12","title":"Equidistribution and freeness on Grassmannians","author":[{"first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning"},{"last_name":"Horesh","full_name":"Horesh, Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal"},{"full_name":"Wilsch, Florian Alexander","last_name":"Wilsch","orcid":"0000-0001-7302-8256","first_name":"Florian Alexander","id":"560601DA-8D36-11E9-A136-7AC1E5697425"}],"issue":"10","date_updated":"2026-08-06T11:07:27Z","status":"public","oa":1,"article_type":"original","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"}],"oa_version":"Preprint","isi":1,"das_tickbox":"0","publication":"Algebra & Number Theory","year":"2022"},{"article_processing_charge":"No","type":"journal_article","department":[{"_id":"TiBr"}],"supplementarymaterial":"no","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.","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2021-03-21T23:01:21Z","citation":{"ista":"Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101.","short":"T.D. Browning, S. Yamagishi, Mathematische Zeitschrift 299 (2021) 1071–1101.","ieee":"T. D. Browning and S. Yamagishi, “Arithmetic of higher-dimensional orbifolds and a mixed Waring problem,” <i>Mathematische Zeitschrift</i>, vol. 299. Springer Nature, pp. 1071–1101, 2021.","ama":"Browning TD, Yamagishi S. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. <i>Mathematische Zeitschrift</i>. 2021;299:1071–1101. doi:<a href=\"https://doi.org/10.1007/s00209-021-02695-w\">10.1007/s00209-021-02695-w</a>","apa":"Browning, T. D., &#38; Yamagishi, S. (2021). Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-021-02695-w\">https://doi.org/10.1007/s00209-021-02695-w</a>","chicago":"Browning, Timothy D, and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00209-021-02695-w\">https://doi.org/10.1007/s00209-021-02695-w</a>.","mla":"Browning, Timothy D., and Shuntaro Yamagishi. “Arithmetic of Higher-Dimensional Orbifolds and a Mixed Waring Problem.” <i>Mathematische Zeitschrift</i>, vol. 299, Springer Nature, 2021, pp. 1071–1101, doi:<a href=\"https://doi.org/10.1007/s00209-021-02695-w\">10.1007/s00209-021-02695-w</a>."},"page":"1071–1101","volume":299,"fulldoi":"https://doi.org/10.1007/s00209-021-02695-w","external_id":{"isi":["000625573800002"]},"file":[{"checksum":"8ed9f49568806894744096dbbca0ad7b","success":1,"content_type":"application/pdf","date_created":"2021-03-22T12:41:26Z","file_id":"9279","file_size":492685,"date_updated":"2021-03-22T12:41:26Z","file_name":"2021_MathZeitschrift_Browning.pdf","relation":"main_file","creator":"dernst","access_level":"open_access"}],"day":"05","has_accepted_license":"1","_id":"9260","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"language":[{"iso":"eng"}],"quality_controlled":"1","publisher":"Springer Nature","project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2","name":"Between rational and integral points"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","researchdata_availability":"no","doi":"10.1007/s00209-021-02695-w","date_published":"2021-03-05T00:00:00Z","publication_status":"published","intvolume":"       299","file_date_updated":"2021-03-22T12:41:26Z","author":[{"last_name":"Browning","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"first_name":"Shuntaro","full_name":"Yamagishi, Shuntaro","last_name":"Yamagishi"}],"scopus_import":"1","title":"Arithmetic of higher-dimensional orbifolds and a mixed Waring problem","month":"03","status":"public","oa":1,"date_updated":"2026-08-06T11:14:26Z","isi":1,"das_tickbox":"0","year":"2021","publication":"Mathematische Zeitschrift","article_type":"original","ddc":["510"],"oa_version":"Published Version","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."}]}]