{
  "id": "1011.1391",
  "version": "v1",
  "published": "2010-11-05T13:25:00.000Z",
  "updated": "2010-11-05T13:25:00.000Z",
  "title": "On Karatsuba's Problem Concerning the Divisor Function $τ(n)$",
  "authors": [
    "M. A. Korolev"
  ],
  "comment": "32 pages",
  "journal": "Monatsh. Math.168(3-4)(2012), 403-441",
  "doi": "10.1007/s00605-011-0362-9",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study an asymptotic behavior of the sum $\\sum\\limits_{n\\le x}\\frac{\\D \\tau(n)}{\\D \\tau(n+a)}$. Here $\\tau(n)$ denotes the number of divisors of $n$ and $a\\ge 1$ is a fixed integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-05T13:25:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26"
    ],
    "keywords": [
      "karatsubas problem concerning",
      "divisor function",
      "asymptotic behavior",
      "fixed integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.1391K"
    }
  }
}