{
  "id": "1804.08826",
  "version": "v1",
  "published": "2018-04-24T03:09:45.000Z",
  "updated": "2018-04-24T03:09:45.000Z",
  "title": "An upper bound for discrete moments of the derivative of the Riemann zeta-function",
  "authors": [
    "Scott Kirila"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Assuming the Riemann hypothesis, we establish an upper bound for the $2k$-th discrete moment of the derivative of the Riemann zeta-function at nontrivial zeros, where $k$ is a positive real number. Our upper bound agrees with conjectures of Gonek and Hejhal and of Hughes, Keating, and O'Connell. This sharpens a result of Milinovich. Our proof builds upon a method of Adam Harper concerning continuous moments of the zeta-function on the critical line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-24T03:09:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26"
    ],
    "keywords": [
      "upper bound",
      "riemann zeta-function",
      "th discrete moment",
      "adam harper concerning continuous moments",
      "derivative"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}