{
  "id": "1703.08315",
  "version": "v1",
  "published": "2017-03-24T08:52:29.000Z",
  "updated": "2017-03-24T08:52:29.000Z",
  "title": "Extreme values of the Riemann zeta function on the 1-line",
  "authors": [
    "Christoph Aistleitner",
    "Kamalakshya Mahatab",
    "Marc Munsch"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that there are arbitrarily large values of $t$ such that $|\\zeta(1+it)| \\geq e^{\\gamma} (\\log_2 t + \\log_3 t) + \\mathcal{O}(1)$. This matches the prediction for the optimal lower bound in a conjecture of Granville and Soundararajan. Our proof uses a new variant of the \"long resonator\" method. While earlier implementations of this method crucially relied on a \"sparsification\" technique to control the mean-square of the resonator function, in the present paper we exploit certain self-similarity properties of a specially designed resonator function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-24T08:52:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "riemann zeta function",
      "extreme values",
      "optimal lower bound",
      "earlier implementations",
      "specially designed resonator function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}