{
  "id": "math/0310231",
  "version": "v1",
  "published": "2003-10-16T00:33:48.000Z",
  "updated": "2003-10-16T00:33:48.000Z",
  "title": "Oppenheim conjecture for pairs consisting of a linear form and a quadratic form",
  "authors": [
    "Alexander Gorodnik"
  ],
  "comment": "To be published in Trans. Amer. Math. Soc., 17 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "Let Q be a nondegenerate quadratic form, and L is a nonzero linear form of dimension d>3. As a generalization of the Oppenheim conjecture, we prove that the set {(Q(x),L(x)):x\\in Z^d} is dense in R^2 provided that Q and L satisfy some natural conditions. The proof uses dynamics on homogeneous spaces of Lie groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-16T00:33:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A17",
      "11J13",
      "11H55"
    ],
    "keywords": [
      "oppenheim conjecture",
      "pairs consisting",
      "nonzero linear form",
      "nondegenerate quadratic form",
      "natural conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10231G"
    }
  }
}