[{"project":[{"call_identifier":"FWF","_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","grant_number":"P32428"}],"status":"public","file_date_updated":"2025-01-09T09:08:14Z","day":"01","language":[{"iso":"eng"}],"author":[{"first_name":"Dante","id":"6A459894-5FDD-11E9-AF35-BB24E6697425","full_name":"Bonolis, Dante","last_name":"Bonolis"},{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","full_name":"Huang, Zhizhong","last_name":"Huang","first_name":"Zhizhong"}],"arxiv":1,"abstract":[{"lang":"eng","text":"We prove the Manin–Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2)."}],"external_id":{"isi":["001204670500001"],"arxiv":["2204.09322"]},"OA_type":"hybrid","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Springer Nature","researchdata_availability":"no","citation":{"chicago":"Bonolis, Dante, Timothy D Browning, and Zhizhong Huang. “Density of Rational Points on Some Quadric Bundle Threefolds.” <i>Mathematische Annalen</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00208-024-02854-4\">https://doi.org/10.1007/s00208-024-02854-4</a>.","ista":"Bonolis D, Browning TD, Huang Z. 2024. Density of rational points on some quadric bundle threefolds. Mathematische Annalen. 390, 4123–4207.","apa":"Bonolis, D., Browning, T. D., &#38; Huang, Z. (2024). Density of rational points on some quadric bundle threefolds. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-024-02854-4\">https://doi.org/10.1007/s00208-024-02854-4</a>","short":"D. Bonolis, T.D. Browning, Z. Huang, Mathematische Annalen 390 (2024) 4123–4207.","ama":"Bonolis D, Browning TD, Huang Z. Density of rational points on some quadric bundle threefolds. <i>Mathematische Annalen</i>. 2024;390:4123-4207. doi:<a href=\"https://doi.org/10.1007/s00208-024-02854-4\">10.1007/s00208-024-02854-4</a>","mla":"Bonolis, Dante, et al. “Density of Rational Points on Some Quadric Bundle Threefolds.” <i>Mathematische Annalen</i>, vol. 390, Springer Nature, 2024, pp. 4123–207, doi:<a href=\"https://doi.org/10.1007/s00208-024-02854-4\">10.1007/s00208-024-02854-4</a>.","ieee":"D. Bonolis, T. D. Browning, and Z. Huang, “Density of rational points on some quadric bundle threefolds,” <i>Mathematische Annalen</i>, vol. 390. Springer Nature, pp. 4123–4207, 2024."},"das_tickbox":"0","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).The authors are grateful to Florian Wilsch for useful comments. While working on this paper the authors were supported by FWF grant P 32428.","supplementarymaterial":"no","_id":"15337","department":[{"_id":"TiBr"}],"doi":"10.1007/s00208-024-02854-4","date_published":"2024-11-01T00:00:00Z","OA_place":"publisher","corr_author":"1","has_accepted_license":"1","page":"4123-4207","article_type":"original","oa_version":"Published Version","ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","license":"https://creativecommons.org/licenses/by/4.0/","oa":1,"month":"11","article_processing_charge":"Yes (via OA deal)","title":"Density of rational points on some quadric bundle threefolds","intvolume":"       390","isi":1,"volume":390,"type":"journal_article","year":"2024","date_updated":"2026-07-29T09:56:42Z","publication_status":"published","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"publication":"Mathematische Annalen","file":[{"access_level":"open_access","checksum":"5dd51531deb1e4760c38c3c0c7d5aedc","file_id":"18796","file_size":1019116,"file_name":"2024_MathAnnalen_Bonolis.pdf","success":1,"date_updated":"2025-01-09T09:08:14Z","date_created":"2025-01-09T09:08:14Z","content_type":"application/pdf","creator":"dernst","relation":"main_file"}],"fulldoi":"https://doi.org/10.1007/s00208-024-02854-4","date_created":"2024-04-21T22:00:53Z"},{"status":"public","language":[{"iso":"eng"}],"author":[{"first_name":"Yang","last_name":"Cao","full_name":"Cao, Yang"},{"last_name":"Huang","id":"21f1b52f-2fd1-11eb-a347-a4cdb9b18a51","full_name":"Huang, Zhizhong","first_name":"Zhizhong"}],"day":"26","arxiv":1,"abstract":[{"lang":"eng","text":"We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate integral quadratic form in  n>3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics."}],"external_id":{"arxiv":["2003.07287"],"isi":["000792517300014"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"108236","issue":"3","researchdata_availability":"no","publisher":"Elsevier","_id":"10765","department":[{"_id":"TiBr"}],"scopus_import":"1","supplementarymaterial":"no","das_tickbox":"0","citation":{"chicago":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>.","ista":"Cao Y, Huang Z. 2022. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. Advances in Mathematics. 398(3), 108236.","apa":"Cao, Y., &#38; Huang, Z. (2022). Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2022.108236\">https://doi.org/10.1016/j.aim.2022.108236</a>","short":"Y. Cao, Z. Huang, Advances in Mathematics 398 (2022).","ama":"Cao Y, Huang Z. Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics. <i>Advances in Mathematics</i>. 2022;398(3). doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>","ieee":"Y. Cao and Z. Huang, “Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics,” <i>Advances in Mathematics</i>, vol. 398, no. 3. Elsevier, 2022.","mla":"Cao, Yang, and Zhizhong Huang. “Arithmetic Purity of the Hardy-Littlewood Property and Geometric Sieve for Affine Quadrics.” <i>Advances in Mathematics</i>, vol. 398, no. 3, 108236, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108236\">10.1016/j.aim.2022.108236</a>."},"acknowledgement":"We are grateful to Mikhail Borovoi, Zeev Rudnick and Olivier Wienberg for their interest in our\r\nwork. We would like to address our gratitude to Ulrich Derenthal for his generous support at Leibniz Universitat Hannover. We are in debt to Tim Browning for an enlightening discussion and to the anonymous referees for critical comments, which lead to overall improvements of various preliminary versions of this paper. Part of this work was carried out and reported during a visit to the University of Science and Technology of China. We thank Yongqi Liang for offering warm hospitality. The first author was supported by a Humboldt-Forschungsstipendium. The second author was supported by grant DE 1646/4-2 of the Deutsche Forschungsgemeinschaft.","date_published":"2022-03-26T00:00:00Z","doi":"10.1016/j.aim.2022.108236","oa_version":"Preprint","article_type":"original","main_file_link":[{"url":"https://arxiv.org/abs/2003.07287","open_access":"1"}],"quality_controlled":"1","corr_author":"1","month":"03","oa":1,"title":"Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics","article_processing_charge":"No","intvolume":"       398","volume":398,"isi":1,"type":"journal_article","year":"2022","publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"publication":"Advances in Mathematics","publication_status":"published","fulldoi":"https://doi.org/10.1016/j.aim.2022.108236","date_created":"2022-02-20T23:01:30Z","date_updated":"2026-08-19T13:00:41Z"}]