{
  "id": "1508.06394",
  "version": "v1",
  "published": "2015-08-26T07:50:10.000Z",
  "updated": "2015-08-26T07:50:10.000Z",
  "title": "On some upper bounds for the zeta-function and the Dirichlet divisor problem",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $d(n)$ be the number of divisors of $n$, let $$ \\Delta(x) := \\sum_{n\\le x}d(n) - x(\\log x + 2\\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\\zeta(s)$ denote the Riemann zeta-function. Several upper bounds for integrals of the type $$ \\int_0^T\\Delta^k(t)|\\zeta(1/2+it)|^{2m}dt \\qquad(k,m\\in\\Bbb N) $$ are given. This complements the results of the paper Ivi\\'c-Zhai [Indag. Math. 2015], where asymptotic formulas for $2\\le k \\le 8,m =1$ were established for the above integral.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-26T07:50:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11N37"
    ],
    "keywords": [
      "upper bounds",
      "classical dirichlet divisor problem",
      "paper ivic-zhai",
      "error term",
      "riemann zeta-function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150806394I"
    }
  }
}