{
  "id": "2102.04038",
  "version": "v1",
  "published": "2021-02-08T07:33:59.000Z",
  "updated": "2021-02-08T07:33:59.000Z",
  "title": "Prime-representing functions and Hausdorff dimension",
  "authors": [
    "Kota Saito"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT",
    "math.MG"
  ],
  "abstract": "In 2010, Matom\\\"{a}ki investigated the set of $A>1$ such that the integer part of $ A^{c^k} $ is a prime number for every $k\\in \\mathbb{N}$, where $c\\geq 2$ is any fixed real number. She proved that the set is uncountable, nowhere dense, and has Lebesgue measure $0$. In this article, we show that the set has Hausdorff dimension $1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-08T07:33:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K55",
      "11A41"
    ],
    "keywords": [
      "hausdorff dimension",
      "prime-representing functions",
      "prime number",
      "lebesgue measure",
      "integer part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}