{"publisher":"Oxford University Press","oa":1,"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:45:31Z","title":"A transference approach to a Roth-type theorem in the squares","quality_controlled":"1","status":"public","article_processing_charge":"No","month":"04","date_updated":"2024-03-05T11:52:36Z","type":"journal_article","day":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1510.00136"}],"abstract":[{"text":"We show that any subset of the squares of positive relative upper density contains nontrivial solutions to a translation-invariant linear equation in five or more variables, with explicit quantitative bounds. As a consequence, we establish the partition regularity of any diagonal quadric in five or more variables whose coefficients sum to zero. Unlike previous approaches, which are limited to equations in seven or more variables, we employ transference technology of Green to import bounds from the linear setting.","lang":"eng"}],"date_published":"2017-04-01T00:00:00Z","publication_status":"published","extern":"1","issue":"7","year":"2017","intvolume":"      2017","publist_id":"7634","volume":2017,"acknowledgement":"Whilst working on this paper the authors were supported by ERC grant 306457.","external_id":{"arxiv":["1510.00136"]},"publication_identifier":{"issn":["1073-7928"]},"doi":"10.1093/imrn/rnw096","page":"2219 - 2248","publication":"International Mathematics Research Notices","author":[{"full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177"},{"first_name":"Sean","last_name":"Prendiville","full_name":"Prendiville, Sean"}],"language":[{"iso":"eng"}],"_id":"268","citation":{"apa":"Browning, T. D., &#38; Prendiville, S. (2017). A transference approach to a Roth-type theorem in the squares. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnw096\">https://doi.org/10.1093/imrn/rnw096</a>","ista":"Browning TD, Prendiville S. 2017. A transference approach to a Roth-type theorem in the squares. International Mathematics Research Notices. 2017(7), 2219–2248.","chicago":"Browning, Timothy D, and Sean Prendiville. “A Transference Approach to a Roth-Type Theorem in the Squares.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2017. <a href=\"https://doi.org/10.1093/imrn/rnw096\">https://doi.org/10.1093/imrn/rnw096</a>.","ama":"Browning TD, Prendiville S. A transference approach to a Roth-type theorem in the squares. <i>International Mathematics Research Notices</i>. 2017;2017(7):2219-2248. doi:<a href=\"https://doi.org/10.1093/imrn/rnw096\">10.1093/imrn/rnw096</a>","short":"T.D. Browning, S. Prendiville, International Mathematics Research Notices 2017 (2017) 2219–2248.","mla":"Browning, Timothy D., and Sean Prendiville. “A Transference Approach to a Roth-Type Theorem in the Squares.” <i>International Mathematics Research Notices</i>, vol. 2017, no. 7, Oxford University Press, 2017, pp. 2219–48, doi:<a href=\"https://doi.org/10.1093/imrn/rnw096\">10.1093/imrn/rnw096</a>.","ieee":"T. D. Browning and S. Prendiville, “A transference approach to a Roth-type theorem in the squares,” <i>International Mathematics Research Notices</i>, vol. 2017, no. 7. Oxford University Press, pp. 2219–2248, 2017."},"article_type":"original"}