{
  "id": "2404.08575",
  "version": "v1",
  "published": "2024-04-12T16:21:57.000Z",
  "updated": "2024-04-12T16:21:57.000Z",
  "title": "Hybrid Statistics of a Random Model of Zeta over Intervals of Varying Length",
  "authors": [
    "Christine Chang"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR",
    "math.NT"
  ],
  "abstract": "Arguin, Dubach & Hartung recently conjectured that an intermediate regime exists between IID and log-correlated statistics for extreme values of a random model of the Riemann zeta function. For the same model, we prove a matching upper and lower tail for the distribution of its maximum. This tail interpolates between that of the two aforementioned regimes. We apply the result to yield a new sharp estimate on moments over short intervals, generalizing a result by Harper. In particular, we observe a hybrid regime for moments with a distinctive transition to the IID regime for intervals of length larger than $\\exp(\\sqrt{\\log \\log T})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-12T16:21:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70",
      "11M06"
    ],
    "keywords": [
      "random model",
      "hybrid statistics",
      "varying length",
      "riemann zeta function",
      "extreme values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}