{"intvolume":"      2017","publist_id":"7646","volume":2017,"year":"2017","acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.","page":"122","doi":"10.1515/crelle-2014-0122","publication":"Journal fur die Reine und Angewandte Mathematik","author":[{"orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning"},{"first_name":"Sean","last_name":"Prendiville","full_name":"Prendiville, Sean"}],"external_id":{"arxiv":["1402.4489"]},"publication_identifier":{"issn":["0075-4102"]},"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.","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>.","short":"T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik 2017 (2017) 122.","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>.","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.","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>","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>"},"article_type":"original","language":[{"iso":"eng"}],"_id":"256","oa":1,"oa_version":"Preprint","date_created":"2018-12-11T11:45:28Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Walter de Gruyter","quality_controlled":"1","title":"Improvements in Birch's theorem on forms in many variables","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"271"}]},"status":"public","type":"journal_article","day":"01","article_processing_charge":"No","month":"10","date_updated":"2024-03-05T12:09:21Z","publication_status":"published","date_published":"2017-10-01T00:00:00Z","extern":"1","issue":"731","main_file_link":[{"url":"https://arxiv.org/abs/1402.4489","open_access":"1"}],"abstract":[{"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.","lang":"eng"}]}