{"extern":"1","type":"journal_article","date_updated":"2024-03-05T12:09:22Z","volume":2017,"publication_identifier":{"issn":["0075-4102"]},"related_material":{"record":[{"relation":"later_version","status":"public","id":"256"}]},"_id":"271","author":[{"last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"last_name":"Prendiville","full_name":"Prendiville, Sean","first_name":"Sean"}],"doi":"10.1515/crelle-2014-0122","abstract":[{"lang":"eng","text":"We show that a non-singular integral form of degree d is soluble non-trivially over the integers if and only if it is soluble non-trivially over the reals and the p-adic numbers, provided that the form has at least (d-\\sqrt{d}/2)2^d variables. This improves on a longstanding result of Birch."}],"publication":"Journal fur die Reine und Angewandte Mathematik","publication_status":"submitted","acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.","article_processing_charge":"No","month":"02","date_created":"2018-12-11T11:45:32Z","citation":{"chicago":"Browning, Timothy D, and Sean Prendiville. “Improvements in Birch’s Theorem on Forms in Many Variables.” <i>Journal Fur Die Reine Und Angewandte Mathematik</i>. Walter de Gruyter, n.d. <a href=\"https://doi.org/10.1515/crelle-2014-0122\">https://doi.org/10.1515/crelle-2014-0122</a>.","ista":"Browning TD, Prendiville S. Improvements in Birch’s theorem on forms in many variables. Journal fur die Reine und Angewandte Mathematik. 2017(731), 203–234.","apa":"Browning, T. D., &#38; Prendiville, S. (n.d.). Improvements in Birch’s theorem on forms in many variables. <i>Journal Fur Die Reine Und Angewandte Mathematik</i>. Walter de Gruyter. <a href=\"https://doi.org/10.1515/crelle-2014-0122\">https://doi.org/10.1515/crelle-2014-0122</a>","ama":"Browning TD, Prendiville S. Improvements in Birch’s theorem on forms in many variables. <i>Journal fur die Reine und Angewandte Mathematik</i>. 2017(731):203-234. doi:<a href=\"https://doi.org/10.1515/crelle-2014-0122\">10.1515/crelle-2014-0122</a>","mla":"Browning, Timothy D., and Sean Prendiville. “Improvements in Birch’s Theorem on Forms in Many Variables.” <i>Journal Fur Die Reine Und Angewandte Mathematik</i>, vol. 2017, no. 731, Walter de Gruyter, pp. 203–34, doi:<a href=\"https://doi.org/10.1515/crelle-2014-0122\">10.1515/crelle-2014-0122</a>.","short":"T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik 2017 (n.d.) 203–234.","ieee":"T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms in many variables,” <i>Journal fur die Reine und Angewandte Mathematik</i>, vol. 2017, no. 731. Walter de Gruyter, pp. 203–234."},"external_id":{"arxiv":["1402.4489"]},"status":"public","page":"203 - 234","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"7631","language":[{"iso":"eng"}],"intvolume":"      2017","quality_controlled":"1","title":"Improvements in Birch's theorem on forms in many variables","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1402.4489"}],"oa_version":"Preprint","issue":"731","day":"20","article_type":"original","publisher":"Walter de Gruyter","year":"2015","date_published":"2015-02-20T00:00:00Z"}