{
  "id": "0708.1601",
  "version": "v2",
  "published": "2007-08-12T08:50:48.000Z",
  "updated": "2009-01-19T08:05:51.000Z",
  "title": "On the mean square of the divisor function in short intervals",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "11 pages",
  "journal": "J. Th\\'eorie des Nombres Bordeaux 21(2009), 195-205",
  "categories": [
    "math.NT"
  ],
  "abstract": "We provide upper bounds for the mean square integral $$ \\int_X^{2X}(\\Delta_k(x+h) - \\Delta_k(x))^2 dx \\qquad(h = h(X)\\gg1, h = o(x) {\\roman{as}} X\\to\\infty) $$ where $h$ lies in a suitable range. For $k\\ge2$ a fixed integer, $\\Delta_k(x)$ is the error term in the asymptotic formula for the summatory function of the divisor function $d_k(n)$, generated by $\\zeta^k(s)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-19T08:05:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11N37"
    ],
    "keywords": [
      "divisor function",
      "short intervals",
      "mean square integral",
      "upper bounds",
      "error term"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.1601I"
    }
  }
}