Power-free values of polynomials on symmetric varieties

Tim D Browning, Alexander Gorodnik

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
283 Downloads (Pure)


Given a symmetric variety Y defined over the rationals 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.
Original languageEnglish
JournalProceedings of the London Mathematical Society
Early online date10 Mar 2017
Publication statusE-pub ahead of print - 10 Mar 2017


  • math.NT
  • math.DS
  • 11N32, 11D09, 11D45, 20G30

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