{
  "id": "0907.1910",
  "version": "v1",
  "published": "2009-07-10T21:01:20.000Z",
  "updated": "2009-07-10T21:01:20.000Z",
  "title": "On the value-distribution of the Riemann zeta-function on the critical line",
  "authors": [
    "Justas Kalpokas",
    "Jörn Steuding"
  ],
  "comment": "16 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the intersections of the curve $\\mathbb{R}\\ni t\\mapsto \\zeta({1\\over 2}+it)$ with the real axis. We show that if the Riemann hypothesis is true, the mean-value of those real values exists and is equal to 1. Moreover, we show unconditionally that the zeta-function takes arbitrarily large real values on the critical line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-10T21:01:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "critical line",
      "riemann zeta-function",
      "value-distribution",
      "arbitrarily large real values",
      "riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.1910K"
    }
  }
}