{
  "id": "math/0610539",
  "version": "v3",
  "published": "2006-10-18T06:35:29.000Z",
  "updated": "2006-10-26T08:23:39.000Z",
  "title": "On the Riemann zeta-function and the divisor problem III",
  "authors": [
    "Aleksandar Ivic"
  ],
  "comment": "18 pages",
  "journal": "Annales Univ. Sci. Budapest., Sect. Comp. 29(2008), 3-23",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Delta(x)$ denote the error term in the Dirichlet divisor problem, and $E(T)$ the error term in the asymptotic formula for the mean square of $|\\zeta(1/2+it)|$. If $E^*(t) = E(t) - 2\\pi\\Delta^*(t/2\\pi)$ with $\\Delta^*(x) = -\\Delta(x) + 2\\Delta(2x) - {1\\over2}\\Delta(4x)$ and we set $\\int_0^T E^*(t) dt = 3\\pi T/4 + R(T)$, then we obtain $$ R(T) = O_\\epsilon(T^{593/912+\\epsilon}), \\int_0^TR^4(t) dt \\ll_\\epsilon T^{3+\\epsilon}, $$ and $$ \\int_0^TR^2(t) dt = T^2P_3(\\log T) + O_\\epsilon(T^{11/6+\\epsilon}), $$ where $P_3(y)$ is a cubic polynomial in $y$ with positive leading coefficient.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-10-26T08:23:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11M06"
    ],
    "keywords": [
      "riemann zeta-function",
      "error term",
      "dirichlet divisor problem",
      "cubic polynomial",
      "asymptotic formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10539I"
    }
  }
}