[{"intvolume":"      2017","status":"public","publication":"Journal fur die Reine und Angewandte Mathematik","quality_controlled":"1","publisher":"Walter de Gruyter","date_created":"2018-12-11T11:45:28Z","month":"10","extern":"1","page":"122","doi":"10.1515/crelle-2014-0122","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"271","relation":"earlier_version","status":"public"}]},"acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.","author":[{"last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"full_name":"Prendiville, Sean","first_name":"Sean","last_name":"Prendiville"}],"type":"journal_article","day":"01","title":"Improvements in Birch's theorem on forms in many variables","citation":{"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>","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>.","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.","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.","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>."},"volume":2017,"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1402.4489","open_access":"1"}],"publication_status":"published","_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."}],"article_processing_charge":"No","issue":"731","arxiv":1,"publication_identifier":{"issn":["0075-4102"]},"external_id":{"arxiv":["1402.4489"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2024-03-05T12:09:21Z","oa_version":"Preprint","year":"2017","article_type":"original","publist_id":"7646"},{"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"}],"arxiv":1,"article_processing_charge":"No","issue":"731","volume":2017,"publication_status":"submitted","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1402.4489"}],"oa":1,"article_type":"original","publist_id":"7631","oa_version":"Preprint","year":"2015","external_id":{"arxiv":["1402.4489"]},"date_updated":"2024-03-05T12:09:22Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0075-4102"]},"month":"02","extern":"1","date_created":"2018-12-11T11:45:32Z","page":"203 - 234","publication":"Journal fur die Reine und Angewandte Mathematik","quality_controlled":"1","intvolume":"      2017","status":"public","publisher":"Walter de Gruyter","day":"20","type":"journal_article","author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning"},{"first_name":"Sean","full_name":"Prendiville, Sean","last_name":"Prendiville"}],"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, pp. 203–34, doi:<a href=\"https://doi.org/10.1515/crelle-2014-0122\">10.1515/crelle-2014-0122</a>.","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.","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.","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>.","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>","short":"T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik 2017 (n.d.) 203–234."},"title":"Improvements in Birch's theorem on forms in many variables","language":[{"iso":"eng"}],"doi":"10.1515/crelle-2014-0122","related_material":{"record":[{"relation":"later_version","id":"256","status":"public"}]},"acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457."}]