{"volume":114,"year":"2017","day":"01","article_type":"original","publisher":"Wiley","status":"public","citation":{"apa":"Browning, T. D., & Gorodnik, A. (2017). Power-free values of polynomials on symmetric varieties. *Proceedings of the London Mathematical Society*. Wiley. https://doi.org/10.1112/plms.12030","ista":"Browning TD, Gorodnik A. 2017. Power-free values of polynomials on symmetric varieties. Proceedings of the London Mathematical Society. 114(6), 1044–1080.","ama":"Browning TD, Gorodnik A. Power-free values of polynomials on symmetric varieties. *Proceedings of the London Mathematical Society*. 2017;114(6):1044-1080. doi:10.1112/plms.12030","ieee":"T. D. Browning and A. Gorodnik, “Power-free values of polynomials on symmetric varieties,” *Proceedings of the London Mathematical Society*, vol. 114, no. 6. Wiley, pp. 1044–1080, 2017.","short":"T.D. Browning, A. Gorodnik, Proceedings of the London Mathematical Society 114 (2017) 1044–1080.","chicago":"Browning, Timothy D, and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” *Proceedings of the London Mathematical Society*. Wiley, 2017. https://doi.org/10.1112/plms.12030.","mla":"Browning, Timothy D., and Alexander Gorodnik. “Power-Free Values of Polynomials on Symmetric Varieties.” *Proceedings of the London Mathematical Society*, vol. 114, no. 6, Wiley, 2017, pp. 1044–80, doi:10.1112/plms.12030."},"publist_id":"7632","_id":"270","oa":1,"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 114","oa_version":"Preprint","title":"Power-free values of polynomials on symmetric varieties","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"full_name":"Gorodnik, Alexander","last_name":"Gorodnik","first_name":"Alexander"}],"page":"1044 - 1080","publication_identifier":{"issn":["0024-6115"]},"language":[{"iso":"eng"}],"publication":"Proceedings of the London Mathematical Society","type":"journal_article","date_created":"2018-12-11T11:45:32Z","corr_author":"1","main_file_link":[{"url":"https://arxiv.org/abs/1606.06342","open_access":"1"}],"doi":"10.1112/plms.12030","date_updated":"2024-10-09T20:58:16Z","external_id":{"arxiv":["1606.06342"]},"date_published":"2017-06-01T00:00:00Z","acknowledgement":"While working on this paper the authors were supported by ERC grants 306457 and 239606, respectively.","quality_controlled":"1","issue":"6","extern":"1","month":"06","publication_status":"published","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"}]}