{
  "id": "0904.0616",
  "version": "v1",
  "published": "2009-04-03T16:33:55.000Z",
  "updated": "2009-04-03T16:33:55.000Z",
  "title": "About statistics of periods of continued fractions of quadratic irrationalities",
  "authors": [
    "E. Yu. Lerner"
  ],
  "comment": "10 pages, 3 figures, 1 table",
  "journal": "Functional Analysis and Other Mathematics, Springer Berlin / Heidelberg, Vol. 3, Issue 1 (2010), pp 75-83",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form $x^2+p x=q$ with integer $p$ and $q$, $p^2+q^2\\le R^2$. Our results concern the average sum of period elements and Gauss--Kuzmin statistics as $R\\to\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-03T16:33:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K50",
      "11J70"
    ],
    "keywords": [
      "continued fractions",
      "quadratic irrationalities",
      "gauss-kuzmin statistics",
      "average sum",
      "quadratic equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0616L"
    }
  }
}