{
  "id": "1812.01415",
  "version": "v1",
  "published": "2018-12-04T13:57:02.000Z",
  "updated": "2018-12-04T13:57:02.000Z",
  "title": "A note on the maximum of the Riemann zeta function on the 1-line",
  "authors": [
    "Winston Heap"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the relationship between the maximum of the zeta function on the 1-line and the maximal order of $S(t)$, the error term in the number of zeros up to height $t$. We show that the conjectured upper bounds on $S(t)$ along with the Riemann hypothesis imply a conjecture of Littlewood that $\\max_{t\\in [1,T]}|\\zeta(1+it)|\\sim e^\\gamma\\log\\log T$. The relationship in the region $1/2<\\sigma<1$ is also investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-04T13:57:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "maximal order",
      "error term",
      "riemann hypothesis",
      "conjectured upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}