{
  "id": "2010.06295",
  "version": "v1",
  "published": "2020-10-13T11:21:24.000Z",
  "updated": "2020-10-13T11:21:24.000Z",
  "title": "Dirichlet series of integers with missing digits",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For certain sequences $A$ of positive integers with missing $g$-adic digits, the Dirichlet series $F_A(s) = \\sum_{a\\in A} a^{-s}$ has abscissa of convergence $\\sigma_c < 1$. The number $\\sigma_c$ is computed. This generalizes and strengthens a classical theorem of Kempner on the convergence of the sum of the reciprocals of a sequence of integers with missing decimal digits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-13T11:21:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "11B05",
      "11B75",
      "11K16"
    ],
    "keywords": [
      "dirichlet series",
      "missing digits",
      "missing decimal digits",
      "adic digits",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}