{"title":"Power-free values of polynomials on symmetric varieties","quality_controlled":"1","status":"public","publisher":"Wiley","oa_version":"Preprint","oa":1,"date_created":"2018-12-11T11:45:32Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.06342"}],"abstract":[{"lang":"eng","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."}],"extern":"1","publication_status":"published","date_published":"2017-06-01T00:00:00Z","issue":"6","month":"06","article_processing_charge":"No","date_updated":"2024-03-05T11:58:25Z","type":"journal_article","day":"01","acknowledgement":"While working on this paper the authors were supported by ERC grants 306457 and 239606, respectively.","year":"2017","intvolume":"       114","volume":114,"publist_id":"7632","_id":"270","language":[{"iso":"eng"}],"article_type":"original","citation":{"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.","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>.","short":"T.D. Browning, A. Gorodnik, Proceedings of the London Mathematical Society 114 (2017) 1044–1080.","ista":"Browning TD, Gorodnik A. 2017. Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. 114(6), 1044–1080.","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>.","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>","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>"},"external_id":{"arxiv":["1606.06342"]},"publication_identifier":{"issn":["0024-6115"]},"author":[{"first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","orcid":"0000-0002-8314-0177"},{"full_name":"Gorodnik, Alexander","first_name":"Alexander","last_name":"Gorodnik"}],"publication":"Proceedings of the London Mathematical Society","page":"1044 - 1080","doi":"10.1112/plms.12030"}