{
  "id": "1606.06342",
  "version": "v1",
  "published": "2016-06-20T21:33:33.000Z",
  "updated": "2016-06-20T21:33:33.000Z",
  "title": "Power-free values of polynomials on symmetric varieties",
  "authors": [
    "T. D. Browning",
    "A. Gorodnik"
  ],
  "comment": "47 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-20T21:33:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N32",
      "11D09",
      "11D45",
      "20G30"
    ],
    "keywords": [
      "symmetric variety",
      "power-free values",
      "integral points",
      "general affine quadrics",
      "uniform upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}