{
  "id": "1611.02424",
  "version": "v1",
  "published": "2016-11-08T08:26:09.000Z",
  "updated": "2016-11-08T08:26:09.000Z",
  "title": "Distribution of class numbers in continued fraction families of real quadratic fields",
  "authors": [
    "Alexander Dahl",
    "Vítězslav Kala"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We construct a random model to study the distribution of class numbers in special families of real quadratic fields $\\mathbb Q(\\sqrt d)$ arising from continued fractions. These families are obtained by considering periodic continued fraction expansions of the form $\\sqrt {D(n)}=[f(n), [u_1, u_2, \\dots, u_{s-1}, 2f(n)]]$ with fixed coefficients $u_1, \\dots, u_{s-1}$ and generalize well-known families such as Chowla's $4n^2+1$, for which analogous results were recently proved by Dahl and Lamzouri.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-08T08:26:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11M20",
      "11A55"
    ],
    "keywords": [
      "real quadratic fields",
      "continued fraction families",
      "class numbers",
      "distribution",
      "considering periodic continued fraction expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}