TY - JOUR
AB - 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.
AU - Browning, Timothy D
AU - Gorodnik, Alexander
ID - 270
IS - 6
JF - Proceedings of the London Mathematical Society
SN - 0024-6115
TI - Power-free values of polynomials on symmetric varieties
VL - 114
ER -