{
  "id": "1407.0776",
  "version": "v2",
  "published": "2014-07-03T04:25:27.000Z",
  "updated": "2014-07-15T10:01:05.000Z",
  "title": "On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansions",
  "authors": [
    "Dylan Airey",
    "Bill Mance"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "Following in the footsteps of P. Erd\\H{o}s and A. R\\'enyi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we consider difference sets associated with various notions of normality and sets of numbers with a prescribed range of digits.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-15T10:01:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hausdorff dimension",
      "cantor series expansions satisfy",
      "difference sets",
      "statistical properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0776A"
    }
  }
}