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