{"publist_id":"7631","date_created":"2018-12-11T11:45:32Z","external_id":{"arxiv":["1402.4489"]},"related_material":{"record":[{"status":"public","relation":"later_version","id":"256"}]},"publication":"Journal fur die Reine und Angewandte Mathematik","acknowledgement":"While working on this paper the authors were supported by the Leverhulme Trust and ERC grant 306457.","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","corr_author":"1","author":[{"first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Prendiville, Sean","first_name":"Sean","last_name":"Prendiville"}],"oa":1,"publication_identifier":{"issn":["0075-4102"]},"language":[{"iso":"eng"}],"page":"203 - 234","extern":"1","article_processing_charge":"No","main_file_link":[{"url":"https://arxiv.org/abs/1402.4489","open_access":"1"}],"intvolume":" 2017","issue":"731","_id":"271","status":"public","year":"2015","doi":"10.1515/crelle-2014-0122","publication_status":"submitted","volume":2017,"date_updated":"2024-10-09T20:58:15Z","day":"20","oa_version":"Preprint","date_published":"2015-02-20T00:00:00Z","quality_controlled":"1","month":"02","publisher":"Walter de Gruyter","title":"Improvements in Birch's theorem on forms in many variables","article_type":"original","arxiv":1,"citation":{"mla":"Browning, Timothy D., and Sean Prendiville. “Improvements in Birch’s Theorem on Forms in Many Variables.” Journal Fur Die Reine Und Angewandte Mathematik, vol. 2017, no. 731, Walter de Gruyter, pp. 203–34, doi:10.1515/crelle-2014-0122.","ieee":"T. D. Browning and S. Prendiville, “Improvements in Birch’s theorem on forms in many variables,” Journal fur die Reine und Angewandte Mathematik, 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.” Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter, n.d. https://doi.org/10.1515/crelle-2014-0122.","short":"T.D. Browning, S. Prendiville, Journal Fur Die Reine Und Angewandte Mathematik 2017 (n.d.) 203–234.","ama":"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. doi:10.1515/crelle-2014-0122","apa":"Browning, T. D., & Prendiville, S. (n.d.). Improvements in Birch’s theorem on forms in many variables. Journal Fur Die Reine Und Angewandte Mathematik. Walter de Gruyter. https://doi.org/10.1515/crelle-2014-0122","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."},"type":"journal_article"}