{
  "id": "1208.1825",
  "version": "v1",
  "published": "2012-08-09T07:04:11.000Z",
  "updated": "2012-08-09T07:04:11.000Z",
  "title": "On the fast Khintchine spectrum in continued fractions",
  "authors": [
    "Fan Ai-Hua",
    "Lingmin Liao",
    "Bao-Wei Wang",
    "Jun Wu"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "For $x\\in [0,1)$, let $x=[a_1(x), a_2(x),...]$ be its continued fraction expansion with partial quotients ${a_n(x), n\\ge 1}$. Let $\\psi : \\mathbb{N} \\rightarrow \\mathbb{N}$ be a function with $\\psi(n)/n\\to \\infty$ as $n\\to \\infty$. In this note, the fast Khintchine spectrum, i.e., the Hausdorff dimension of the set $$ E(\\psi):=\\Big{x\\in [0,1): \\lim_{n\\to\\infty}\\frac{1}{\\psi(n)}\\sum_{j=1}^n\\log a_j(x)=1\\Big} $$ is completely determined without any extra condition on $\\psi$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-09T07:04:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fast khintchine spectrum",
      "extra condition",
      "partial quotients",
      "hausdorff dimension",
      "continued fraction expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1825A"
    }
  }
}