{
  "id": "2107.13636",
  "version": "v1",
  "published": "2021-07-28T20:48:50.000Z",
  "updated": "2021-07-28T20:48:50.000Z",
  "title": "A note on the mean values of the derivatives of $ζ'/ζ$",
  "authors": [
    "Andrés Chirre"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Assuming the Riemann hypothesis, we obtain a formula for the mean value of the $k$-derivative of $\\zeta'/\\zeta$, depending on the pair correlation of zeros of the Riemann zeta-function. This formula allows us to obtain new equivalences to Montgomery's pair correlation conjecture. This extends a result of Goldston, Gonek, and Montgomery where the mean value of $\\zeta'/\\zeta$ was considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-28T20:48:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26"
    ],
    "keywords": [
      "mean value",
      "montgomerys pair correlation conjecture",
      "derivative",
      "riemann hypothesis",
      "riemann zeta-function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}