{
  "id": "0907.3803",
  "version": "v1",
  "published": "2009-07-22T09:20:34.000Z",
  "updated": "2009-07-22T09:20:34.000Z",
  "title": "On the integral of Hardy's function",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "7 pages",
  "journal": "Archiv der Mathematik 83(2004), 41-47",
  "categories": [
    "math.NT"
  ],
  "abstract": "If $Z(t) = \\chi^{-1/2}(1/2+it)\\zeta(1/2+it)$ denotes Hardy's function, where $\\zeta(s) = \\chi(s)\\zeta(1-s)$ is the functional equation of the Riemann zeta-function, then it is proved that $$ \\int_0^T Z(t)\\d t = O_\\e(T^{1/4+\\e}). $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-22T09:20:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "denotes hardys function",
      "functional equation",
      "riemann zeta-function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.3803I"
    }
  }
}