{
  "id": "1606.01179",
  "version": "v1",
  "published": "2016-06-03T16:39:28.000Z",
  "updated": "2016-06-03T16:39:28.000Z",
  "title": "An estimate of the second moment of a sampling of the Riemann zeta function on the critical line",
  "authors": [
    "Sihun Jo",
    "Minsuk Yang"
  ],
  "comment": "13 pages",
  "journal": "J. Math. Anal. Appl. 415 (2014) 121-134",
  "doi": "10.1016/j.jmaa.2014.01.040",
  "categories": [
    "math.CA"
  ],
  "abstract": "We investigate the second moment of a random sampling $\\zeta(1/2+iX_t)$ of the Riemann zeta function on the critical line. Our main result states that if $X_t$ is an increasing random sampling with gamma distribution, then for all sufficiently large $t$, \\[\\mathbb{E} |\\zeta(1/2+iX_t)|^2 = \\log t + O(\\sqrt{\\log t}\\log\\log t).\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-03T16:39:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "second moment",
      "critical line",
      "main result states",
      "random sampling"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}