{
  "id": "2411.05573",
  "version": "v1",
  "published": "2024-11-08T13:53:56.000Z",
  "updated": "2024-11-08T13:53:56.000Z",
  "title": "The second moment of the Riemann zeta function at its local extrema",
  "authors": [
    "Christopher Hughes",
    "Solomon Lugmayer",
    "Andrew Pearce-Crump"
  ],
  "comment": "22 pages, 9 figures, 2 tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "Conrey and Ghosh studied the second moment of the Riemann zeta function, evaluated at its local extrema along the critical line, finding the leading order behaviour to be $\\frac{e^2 - 5}{2 \\pi} T (\\log T)^2$. This problem is closely related to a mixed moment of the Riemann zeta function and its derivative. We present a new approach which will uncover the lower order terms for the second moment as a descending chain of powers of logarithms in the asymptotic expansion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-08T13:53:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "riemann zeta function",
      "second moment",
      "local extrema",
      "lower order terms",
      "leading order behaviour"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}