{
  "id": "1511.07140",
  "version": "v1",
  "published": "2015-11-23T09:04:47.000Z",
  "updated": "2015-11-23T09:04:47.000Z",
  "title": "On a cubic moment of Hardy's function with a shift",
  "authors": [
    "Aleksandar Ivić"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "An asymptotic formula for $$ \\int_{T/2}^{T}Z^2(t)Z(t+U)\\,dt\\qquad(0< U = U(T) \\le T^{1/2-\\varepsilon}) $$ is derived, where $$ Z(t) := \\zeta(1/2+it){\\bigl(\\chi(1/2+it)\\bigr)}^{-1/2}\\quad(t\\in\\Bbb R), \\quad \\zeta(s) = \\chi(s)\\zeta(1-s) $$ is Hardy's function. The cubic moment of $Z(t)$ is also discussed, and a mean value result is presented which supports the author's conjecture that $$ \\int_1^TZ^3(t)\\,dt \\;=\\;O_\\varepsilon(T^{3/4+\\varepsilon}). $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-23T09:04:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11N37"
    ],
    "keywords": [
      "hardys function",
      "cubic moment",
      "mean value result",
      "authors conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151107140I"
    }
  }
}