{
  "id": "1305.2028",
  "version": "v1",
  "published": "2013-05-09T08:20:22.000Z",
  "updated": "2013-05-09T08:20:22.000Z",
  "title": "On some mean value results for the zeta-function in short intervals",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\Delta(x)$ denote the error term in the Dirichlet divisor problem, and let $E(T)$ denote 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 $\\Delta^*(x) := -\\Delta(x) + 2\\Delta(2x) - \\frac{1}{2}\\Delta(4x)$ and $\\int_0^T E^*(t)\\,dt = \\frac{3}{4}\\pi T + R(T)$, then we obtain a number of results involving the moments of $|\\zeta(1/2+it)|$ in short intervals, by connecting them to the moments of $E^*(T)$ and $R(T)$ in short intervals. Upper bounds and asymptotic formulas for integrals of the form $$ \\int_T^{2T}\\left(\\int_{t-H}^{t+H}|\\zeta(1/2+iu)|^2\\,du\\right)^k\\,dt \\qquad(k\\in N, 1 \\ll H \\le T) $$ are also treated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-09T08:20:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "mean value results",
      "short intervals",
      "zeta-function",
      "asymptotic formula",
      "error term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2028I"
    }
  }
}