{
  "id": "math/0605721",
  "version": "v2",
  "published": "2006-05-29T09:47:25.000Z",
  "updated": "2006-06-02T14:24:03.000Z",
  "title": "The Laplace and Mellin transforms of powers of the Riemann zeta-function",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "20 pages",
  "journal": "International J. of Mathematics and Analysis Vol. 1 No. 2, 2006, pp. 131-140",
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper gives a survey of known results concerning the Laplace transform $$ L_k(s) := \\int_0^\\infty |\\zeta(1/2+ ix)|^{2k}{\\rm e}^{-sx}{\\rm d} x \\qquad(k \\in N, \\R s > 0), $$ and the (modified) Mellin transform $$ {\\cal Z}_k(s) := \\int_1^\\infty|\\zeta(1/2+ ix)|^{2k}x^{-s}{\\rm d} x\\qquad(k\\in N), $$ where the integral is absolutely convergent for $\\R s \\ge c(k) > 1$. Also some new results on these integral transforms of $|\\zeta(1/2+ ix)|^{2k}$ are given, which have important connections with power moments of the Riemann zeta-function $\\zeta(s)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-02T14:24:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11F72"
    ],
    "keywords": [
      "mellin transform",
      "riemann zeta-function",
      "integral transforms",
      "laplace transform",
      "power moments"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5721I"
    }
  }
}