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