{
  "id": "0812.0330",
  "version": "v1",
  "published": "2008-12-01T17:15:03.000Z",
  "updated": "2008-12-01T17:15:03.000Z",
  "title": "Polynomial parametrization of the solutions of Diophantine equations of genus 0",
  "authors": [
    "Sophie Frisch",
    "Günter Lettl"
  ],
  "comment": "Dedicated to Prof. W. Narkiewicz on the occasion of his 70th birthday. To appear in Functiones et Approximatio. 4 pages",
  "journal": "Funct. Approx. Comment. Math. 39 (2008), part 2, 205-209",
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "Let f in Z[X,Y,Z] be a non-constant, absolutely irreducible, homogeneous polynomial with integer coefficients, such that the projective curve given by f=0 has a function field isomorphic to the rational function field Q(t). We show that all integral solutions of the Diophantine equation f=0 (up to those corresponding to some singular points) can be parametrized by a single triple of integer-valued polynomials. In general, it is not possible to parametrize this set of solutions by a single triple of polynomials with integer coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-01T17:15:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D85",
      "13F20",
      "11D41",
      "14H05"
    ],
    "keywords": [
      "diophantine equation",
      "polynomial parametrization",
      "integer coefficients",
      "single triple",
      "function field isomorphic"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.0330F"
    }
  }
}