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