{
  "id": "1601.02202",
  "version": "v1",
  "published": "2016-01-10T11:52:40.000Z",
  "updated": "2016-01-10T11:52:40.000Z",
  "title": "Limit theorems related to beta-expansion and continued fraction expansion",
  "authors": [
    "Lulu Fang",
    "Min Wu",
    "Bing Li"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "Let $\\beta > 1$ be a real number and $x \\in [0,1)$ be an irrational number. Denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $\\beta$-expansion of $x$ ($n \\in \\mathbb{N}$). In this paper, we show a central limit theorem and a law of the iterated logarithm for the random variables sequence $\\{k_n, n \\geq 1\\}$, which generalize the results of Faivre and Wu respectively from $\\beta =10$ to any $\\beta >1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-10T11:52:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continued fraction expansion",
      "beta-expansion",
      "central limit theorem",
      "random variables sequence",
      "irrational number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102202F"
    }
  }
}