[{"issue":"731","publication_identifier":{"issn":["0075-4102"]},"status":"public","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>.","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>","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.","short":"T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik 2017 (2017) 122.","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."},"intvolume":"      2017","main_file_link":[{"url":"https://arxiv.org/abs/1402.4489","open_access":"1"}],"title":"Improvements in Birch's theorem on forms in many variables","_id":"256","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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."}],"acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.","page":"122","author":[{"orcid":"0000-0002-8314-0177","last_name":"Browning","full_name":"Browning, Timothy D","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Prendiville","first_name":"Sean","full_name":"Prendiville, Sean"}],"day":"01","publist_id":"7646","publication_status":"published","arxiv":1,"date_created":"2018-12-11T11:45:28Z","related_material":{"record":[{"id":"271","relation":"earlier_version","status":"public"}]},"language":[{"iso":"eng"}],"year":"2017","date_published":"2017-10-01T00:00:00Z","type":"journal_article","volume":2017,"oa_version":"Preprint","article_type":"original","external_id":{"arxiv":["1402.4489"]},"publisher":"Walter de Gruyter","date_updated":"2024-03-05T12:09:21Z","doi":"10.1515/crelle-2014-0122","publication":"Journal fur die Reine und Angewandte Mathematik","article_processing_charge":"No","oa":1,"quality_controlled":"1","extern":"1","month":"10"},{"_id":"271","title":"Improvements in Birch's theorem on forms in many variables","abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1402.4489","open_access":"1"}],"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>.","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>.","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.","short":"T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik 2017 (n.d.) 203–234.","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>"},"intvolume":"      2017","issue":"731","publication_identifier":{"issn":["0075-4102"]},"publication":"Journal fur die Reine und Angewandte Mathematik","date_updated":"2024-03-05T12:09:22Z","publisher":"Walter de Gruyter","doi":"10.1515/crelle-2014-0122","article_processing_charge":"No","extern":"1","oa":1,"quality_controlled":"1","month":"02","volume":2017,"date_published":"2015-02-20T00:00:00Z","type":"journal_article","external_id":{"arxiv":["1402.4489"]},"article_type":"original","oa_version":"Preprint","language":[{"iso":"eng"}],"year":"2015","related_material":{"record":[{"status":"public","relation":"later_version","id":"256"}]},"page":"203 - 234","author":[{"orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D"},{"first_name":"Sean","full_name":"Prendiville, Sean","last_name":"Prendiville"}],"publist_id":"7631","publication_status":"submitted","day":"20","arxiv":1,"date_created":"2018-12-11T11:45:32Z"}]