{
  "id": "math/0510404",
  "version": "v3",
  "published": "2005-10-19T02:37:56.000Z",
  "updated": "2007-04-10T23:32:16.000Z",
  "title": "Equidistribution and generalized Mahler measures",
  "authors": [
    "Lucien Szpiro",
    "Thomas J. Tucker"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "Let g be a nonconstant rational map from the projective line to itself that has degree greater than one and is defined over a number field. The map g gives rise to generalized Mahler measures for polynomials in one variable. We use diophantine approximation to show that the generalized Mahler measure of a polynomial F at a place v can be computed by averaging the log of the v-adic absolute value of F over the periodic points of g. This allows us to compute canonical heights of algebraic points via equidistribution on periodic points.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-04-10T23:32:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "11J68",
      "37F10"
    ],
    "keywords": [
      "generalized mahler measure",
      "equidistribution",
      "periodic points",
      "v-adic absolute value",
      "nonconstant rational map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10404S"
    }
  }
}