{
  "id": "math/0305179",
  "version": "v3",
  "published": "2003-05-13T08:30:57.000Z",
  "updated": "2003-11-10T11:51:10.000Z",
  "title": "A mean value result involving the fourth moment of $|ζ(1/2+it)|$",
  "authors": [
    "Aleksandar Ivic"
  ],
  "comment": "9 pages, only TeX formatting corrected",
  "journal": "Annales Univ. Sci. Budapest, Sect. Computatorica 23(2004), 47-58",
  "categories": [
    "math.NT"
  ],
  "abstract": "If $(k,\\ell)$ is an exponent pair such that $k+\\ell<1$, then we have $$ \\int_1^T|\\zeta(1/2+it)|^4|\\zeta(\\sigma+it)|^2dt \\ll_\\epsilon T^{1+\\epsilon}\\quad(\\sigma > \\min({5\\over6},\\max(\\ell-k, {5k+\\ell\\over4k+1})), $$ while if $(k,\\ell)$ is an exponent pair such that $3k+\\ell<1$, then we have $$ \\int_1^T|\\zeta(1/2+it)|^4|\\zeta(\\sigma+it)|^4dt \\ll_\\epsilon T^{1+\\epsilon}\\quad(\\sigma > {11k+\\ell+1\\over8k+2}). $$",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-11-10T11:51:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "mean value result",
      "fourth moment",
      "exponent pair"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5179I"
    }
  }
}