{
  "id": "1710.08990",
  "version": "v1",
  "published": "2017-10-24T21:01:19.000Z",
  "updated": "2017-10-24T21:01:19.000Z",
  "title": "Quadratic Irrationals, Generating Functions, and Lévy Constants",
  "authors": [
    "Anna Belova",
    "Peter Hazard"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT",
    "math.CO",
    "math.DS"
  ],
  "abstract": "We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer coefficients. Consequently we can compute the L\\'evy constant of any quadratic irrational explicitly in terms of its partial quotients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-24T21:01:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11K50",
      "05A15"
    ],
    "keywords": [
      "quadratic irrational",
      "generating function",
      "lévy constants",
      "best rational approximants",
      "rational function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}