Power-free Values of Polynomials on Symmetric Varieties

  title={Power-free Values of Polynomials on Symmetric Varieties},
  author={Tim D. Browning and Alexander Gorodnik},
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… CONTINUE READING

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