{"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file":[{"date_updated":"2021-03-22T12:41:26Z","file_size":492685,"date_created":"2021-03-22T12:41:26Z","checksum":"8ed9f49568806894744096dbbca0ad7b","creator":"dernst","file_name":"2021_MathZeitschrift_Browning.pdf","relation":"main_file","content_type":"application/pdf","file_id":"9279","success":1,"access_level":"open_access"}],"article_type":"original","publisher":"Springer Nature","department":[{"_id":"TiBr"}],"oa":1,"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"}],"oa_version":"Published Version","date_published":"2021-03-05T00:00:00Z","file_date_updated":"2021-03-22T12:41:26Z","publication_identifier":{"eissn":["1432-1823"],"issn":["0025-5874"]},"date_created":"2021-03-21T23:01:21Z","language":[{"iso":"eng"}],"article_processing_charge":"No","title":"Arithmetic of higher-dimensional orbifolds and a mixed Waring problem","page":"1071–1101","day":"05","project":[{"name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2"}],"intvolume":"       299","isi":1,"license":"https://creativecommons.org/licenses/by/4.0/","publication_status":"published","volume":299,"ddc":["510"],"scopus_import":"1","month":"03","publication":"Mathematische Zeitschrift","citation":{"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.","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>.","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>","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>.","ista":"Browning TD, Yamagishi S. 2021. Arithmetic of higher-dimensional orbifolds and a mixed Waring problem. Mathematische Zeitschrift. 299, 1071–1101."},"status":"public","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.","external_id":{"isi":["000625573800002"]},"author":[{"orcid":"0000-0002-8314-0177","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","full_name":"Browning, Timothy D"},{"full_name":"Yamagishi, Shuntaro","first_name":"Shuntaro","last_name":"Yamagishi"}],"date_updated":"2023-08-07T14:20:00Z","has_accepted_license":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","year":"2021","_id":"9260","doi":"10.1007/s00209-021-02695-w","quality_controlled":"1"}