{
  "id": "2201.12974",
  "version": "v1",
  "published": "2022-01-31T03:01:35.000Z",
  "updated": "2022-01-31T03:01:35.000Z",
  "title": "Dimensions of certain sets of continued fractions with non-decreasing partial quotients",
  "authors": [
    "Lulu Fang",
    "Jihua Ma",
    "Kunkun Song",
    "Min Wu"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $[a_1(x),a_2(x),a_3(x),\\cdots]$ be the continued fraction expansion of $x\\in (0,1)$. This paper is concerned with certain sets of continued fractions with non-decreasing partial quotients. As a main result, we obtain the Hausdorff dimension of the set \\[\\left\\{x\\in(0,1): a_1(x)\\leq a_2(x)\\leq \\cdots,\\ \\limsup\\limits_{n\\to\\infty}\\frac{\\log a_n(x)}{\\psi(n)}=1\\right\\}\\] for any $\\psi:\\mathbb{N}\\rightarrow\\mathbb{R}^+$ satisfying $\\psi(n)\\to\\infty$ as $n\\to\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-31T03:01:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K50",
      "28A80"
    ],
    "keywords": [
      "non-decreasing partial quotients",
      "main result",
      "hausdorff dimension",
      "continued fraction expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}