{
  "id": "math/0311403",
  "version": "v1",
  "published": "2003-11-23T11:45:03.000Z",
  "updated": "2003-11-23T11:45:03.000Z",
  "title": "On mean values of some zeta-functions in the critical strip",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "To the memory of R.A. Rankin, 15 pages",
  "journal": "Journal de Th\\'eorie des Nombres de Bordeaux 15(2003), 163-178",
  "categories": [
    "math.NT"
  ],
  "abstract": "For a fixed integer $k\\ge 3$ and fixed $1/2 < \\sigma > 1$ we consider $$ \\int_1^T |\\zeta(\\sigma + it)|^{2k}dt = \\sum_{n=1}^\\infty d_k^2(n)n^{-2\\sigma}T + R(k,\\sigma;T), $$ where $R(k,\\sigma;T) = o(T) (T\\to\\infty)$ is the error term in the above asymptotic formula. Hitherto the sharpest bounds for $R(k,\\sigma;T)$ are given for certain ranges of $\\sigma$. We also obtain new mean value results for the zeta-functions of holomorphic cusp forms and the Rankin-Selberg series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-11-23T11:45:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11F30",
      "11F66"
    ],
    "keywords": [
      "critical strip",
      "zeta-functions",
      "mean value results",
      "holomorphic cusp forms",
      "sharpest bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11403I"
    }
  }
}