{
  "id": "1612.08575",
  "version": "v1",
  "published": "2016-12-27T11:14:49.000Z",
  "updated": "2016-12-27T11:14:49.000Z",
  "title": "Maximum of the Riemann zeta function on a short interval of the critical line",
  "authors": [
    "Louis-Pierre Arguin",
    "David Belius",
    "Paul Bourgade",
    "Maksym Radziwiłł",
    "Kannan Soundararajan"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR",
    "math.NT"
  ],
  "abstract": "We prove the leading order of a conjecture by Fyodorov, Hiary and Keating, about the maximum of the Riemann zeta function on random intervals along the critical line. More precisely, if $t$ is uniformly distributed in $[T,2T]$, then $$ \\max_{|t-u|\\leq 1}\\log\\left|\\zeta\\left(\\frac{1}{2}+\\mathrm{i} u\\right)\\right|=(1+{\\mathrm o}(1))\\log\\log T $$ with probability converging to 1 as $T\\to\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-27T11:14:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70",
      "11M06"
    ],
    "keywords": [
      "riemann zeta function",
      "critical line",
      "short interval",
      "random intervals",
      "leading order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}