{"page":"83 - 115","article_processing_charge":"No","abstract":[{"text":"For any n ≧ 2, let F ∈ ℤ [ x 1, … , xn ] be a form of degree d≧ 2, which produces a geometrically irreducible hypersurface in ℙn–1. This paper is concerned with the number N(F;B) of rational points on F = 0 which have height at most B. For any ε &gt; 0 we establish the estimate N(F; B) = O(B n− 2+ ε ), whenever either n ≦ 5 or the hypersurface is not a union of lines. Here the implied constant depends at most upon d, n and ε.","lang":"eng"}],"publication_status":"published","external_id":{"arxiv":["abs/math/0404456"]},"title":"Counting rational points on hypersurfaces","extern":"1","author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Heath Brown, Roger","last_name":"Heath Brown","first_name":"Roger"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"repository","main_file_link":[{"url":"https://arxiv.org/abs/0707.2296","open_access":"1"}],"year":"2005","date_created":"2018-12-11T11:45:14Z","issue":"584","publication_identifier":{"issn":["0075-4102"]},"doi":"https://doi.org/10.1515/crll.2005.2005.584.83","publication":"Journal fur die Reine und Angewandte Mathematik","oa":1,"month":"11","language":[{"iso":"eng"}],"date_published":"2005-11-26T00:00:00Z","arxiv":1,"publisher":"Walter de Gruyter and Co ","date_updated":"2026-08-21T09:31:08Z","article_type":"original","oa_version":"None","type":"journal_article","publist_id":"7701","_id":"212","citation":{"short":"T.D. Browning, R. Heath Brown, Journal Fur Die Reine Und Angewandte Mathematik (2005) 83–115.","ieee":"T. D. Browning and R. Heath Brown, “Counting rational points on hypersurfaces,” <i>Journal fur die Reine und Angewandte Mathematik</i>, no. 584. Walter de Gruyter and Co , pp. 83–115, 2005.","ista":"Browning TD, Heath Brown R. 2005. Counting rational points on hypersurfaces. Journal fur die Reine und Angewandte Mathematik. (584), 83–115.","ama":"Browning TD, Heath Brown R. Counting rational points on hypersurfaces. <i>Journal fur die Reine und Angewandte Mathematik</i>. 2005;(584):83-115. doi:<a href=\"https://doi.org/10.1515/crll.2005.2005.584.83\">https://doi.org/10.1515/crll.2005.2005.584.83</a>","apa":"Browning, T. D., &#38; Heath Brown, R. (2005). Counting rational points on hypersurfaces. <i>Journal Fur Die Reine Und Angewandte Mathematik</i>. Walter de Gruyter and Co . <a href=\"https://doi.org/10.1515/crll.2005.2005.584.83\">https://doi.org/10.1515/crll.2005.2005.584.83</a>","chicago":"Browning, Timothy D, and Roger Heath Brown. “Counting Rational Points on Hypersurfaces.” <i>Journal Fur Die Reine Und Angewandte Mathematik</i>. Walter de Gruyter and Co , 2005. <a href=\"https://doi.org/10.1515/crll.2005.2005.584.83\">https://doi.org/10.1515/crll.2005.2005.584.83</a>.","mla":"Browning, Timothy D., and Roger Heath Brown. “Counting Rational Points on Hypersurfaces.” <i>Journal Fur Die Reine Und Angewandte Mathematik</i>, no. 584, Walter de Gruyter and Co , 2005, pp. 83–115, doi:<a href=\"https://doi.org/10.1515/crll.2005.2005.584.83\">https://doi.org/10.1515/crll.2005.2005.584.83</a>."},"OA_type":"green","day":"26","status":"public"}