{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.06342"}],"_id":"270","article_type":"original","oa":1,"year":"2017","date_published":"2017-06-01T00:00:00Z","publication_status":"published","acknowledgement":"While working on this paper the authors were supported by ERC grants 306457 and 239606, respectively.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1606.06342"]},"day":"01","publist_id":"7632","date_updated":"2024-03-05T11:58:25Z","issue":"6","citation":{"apa":"Browning, T. D., &#38; Gorodnik, A. (2017). Power-free values of polynomials on symmetric varieties. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.12030\">https://doi.org/10.1112/plms.12030</a>","mla":"Browning, Timothy D., and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” <i>Proceedings of the London Mathematical Society</i>, vol. 114, no. 6, Wiley, 2017, pp. 1044–80, doi:<a href=\"https://doi.org/10.1112/plms.12030\">10.1112/plms.12030</a>.","chicago":"Browning, Timothy D, and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2017. <a href=\"https://doi.org/10.1112/plms.12030\">https://doi.org/10.1112/plms.12030</a>.","short":"T.D. Browning, A. Gorodnik, Proceedings of the London Mathematical Society 114 (2017) 1044–1080.","ama":"Browning TD, Gorodnik A. Power-free values of polynomials on symmetric varieties. <i>Proceedings of the London Mathematical Society</i>. 2017;114(6):1044-1080. doi:<a href=\"https://doi.org/10.1112/plms.12030\">10.1112/plms.12030</a>","ieee":"T. D. Browning and A. Gorodnik, “Power-free values of polynomials on symmetric varieties,” <i>Proceedings of the London Mathematical Society</i>, vol. 114, no. 6. Wiley, pp. 1044–1080, 2017.","ista":"Browning TD, Gorodnik A. 2017. Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. 114(6), 1044–1080."},"language":[{"iso":"eng"}],"month":"06","abstract":[{"text":"Given a symmetric variety Y defined over Q and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski dense set of integral points on Y . We also establish an asymptotic counting formula for this set. In the special case that Y is a quadric hypersurface, we give explicit bounds on the size of r by combining the argument with a uniform upper bound for the density of integral points on general affine quadrics defined over Q.","lang":"eng"}],"publication":"Proceedings of the London Mathematical Society","article_processing_charge":"No","volume":114,"oa_version":"Preprint","quality_controlled":"1","page":"1044 - 1080","extern":"1","date_created":"2018-12-11T11:45:32Z","title":"Power-free values of polynomials on symmetric varieties","type":"journal_article","doi":"10.1112/plms.12030","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","last_name":"Browning","first_name":"Timothy D","full_name":"Browning, Timothy D"},{"first_name":"Alexander","full_name":"Gorodnik, Alexander","last_name":"Gorodnik"}],"intvolume":"       114","publisher":"Wiley","status":"public","publication_identifier":{"issn":["0024-6115"]}}