{
  "id": "math/0701202",
  "version": "v2",
  "published": "2007-01-07T08:47:37.000Z",
  "updated": "2007-01-21T08:54:55.000Z",
  "title": "On the Riemann zeta-function and the divisor problem IV",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "11 pages",
  "journal": "Uniform Distribution Theory 1(2006), 125-135",
  "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 $\\Delta^*(x) = -\\Delta(x) + 2\\Delta(2x) - {1\\over2}\\Delta(4x)$, then it is proved that $$ \\int_0^T|E^*(t)|^3dt \\ll_\\epsilon T^{3/2+\\epsilon}, $$ which is (up to `$\\epsilon$' best possible) and $\\zeta(1/2+it) \\ll_\\epsilon t^{\\rho/2+\\epsilon}$ if $E^*(t) \\ll_\\epsilon t^{\\rho+\\epsilon}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-21T08:54:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N37",
      "11M06"
    ],
    "keywords": [
      "riemann zeta-function",
      "error term",
      "dirichlet divisor problem",
      "asymptotic formula"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1202I"
    }
  }
}