{"quality_controlled":"1","external_id":{"arxiv":["1402.4489"]},"publication":"Journal fur die Reine und Angewandte Mathematik","day":"01","status":"public","publication_identifier":{"issn":["0075-4102"]},"date_published":"2017-10-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1402.4489"}],"doi":"10.1515/crelle-2014-0122","citation":{"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, p. 122, 2017.","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;2017(731):122. doi:<a href=\"https://doi.org/10.1515/crelle-2014-0122\">10.1515/crelle-2014-0122</a>","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, 2017. <a href=\"https://doi.org/10.1515/crelle-2014-0122\">https://doi.org/10.1515/crelle-2014-0122</a>.","apa":"Browning, T. D., &#38; Prendiville, S. (2017). 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>","short":"T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik 2017 (2017) 122.","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, 2017, p. 122, doi:<a href=\"https://doi.org/10.1515/crelle-2014-0122\">10.1515/crelle-2014-0122</a>.","ista":"Browning TD, Prendiville S. 2017. Improvements in Birch’s theorem on forms in many variables. Journal fur die Reine und Angewandte Mathematik. 2017(731), 122."},"abstract":[{"lang":"eng","text":"We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over ℝ and over ℚp for all primes p, provided that the form has at least (d - 1/2 √d)2d variables. This improves on a longstanding result of Birch."}],"publist_id":"7646","publisher":"Walter de Gruyter","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"271"}]},"article_processing_charge":"No","issue":"731","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Improvements in Birch's theorem on forms in many variables","_id":"256","date_created":"2018-12-11T11:45:28Z","page":"122","month":"10","date_updated":"2024-03-05T12:09:21Z","volume":2017,"type":"journal_article","year":"2017","author":[{"orcid":"0000-0002-8314-0177","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","full_name":"Browning, Timothy D"},{"first_name":"Sean","last_name":"Prendiville","full_name":"Prendiville, Sean"}],"article_type":"original","acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.","oa_version":"Preprint","oa":1,"publication_status":"published","extern":"1","intvolume":"      2017"}