{
  "id": "1001.1824",
  "version": "v3",
  "published": "2010-01-12T09:07:03.000Z",
  "updated": "2010-11-11T09:30:26.000Z",
  "title": "On the Mellin transforms of powers of Hardy's function",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "26 pages",
  "journal": "Hardy-Ramanujan Journal 33(2010), 32-58",
  "categories": [
    "math.NT"
  ],
  "abstract": "Various properties of the Mellin transform function $$ {\\cal M}_k(s) := \\int_1^\\infty Z^k(x)x^{-s}dx $$ are investigated, where $$ Z(t) := \\zeta(1/2+it){\\bigl(\\chi(1/2+it)\\bigr)}^{-1/2}, \\quad \\zeta(s) = \\chi(s)\\zeta(1-s) $$ is Hardy's function and $\\zeta(s)$ is Riemann's zeta-function. Connections with power moments of $|\\zeta(1/2+it)|$ are established, and natural boundaries of ${\\cal M}_k(s)$ are discussed.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-11-11T09:30:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "hardys function",
      "mellin transform function",
      "riemanns zeta-function",
      "natural boundaries"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.1824I"
    }
  }
}