@article{270,
abstract = {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.},
author = {Browning, Timothy D and Gorodnik, Alexander},
issn = {0024-6115},
journal = {Proceedings of the London Mathematical Society},
number = {6},
pages = {1044 -- 1080},
publisher = {Wiley},
title = {{Power-free values of polynomials on symmetric varieties}},
doi = {10.1112/plms.12030},
volume = {114},
year = {2017},
}