{
  "id": "1011.5339",
  "version": "v2",
  "published": "2010-11-24T11:20:43.000Z",
  "updated": "2014-05-26T12:24:52.000Z",
  "title": "On the roots of the equation $ζ(s)=a$",
  "authors": [
    "R. Garunkstis",
    "J. Steuding"
  ],
  "comment": "15 pages",
  "journal": "Abh. Math. Semin. Univ. Hambg. 84 (2014), 1-15",
  "doi": "10.1007/s12188-014-0093-7",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given any complex number $a$, we prove that there are infinitely many simple roots of the equation $\\zeta(s)=a$ with arbitrarily large imaginary part. Besides, we give a heuristic interpretation of a certain regularity of the graph of the curve $t\\mapsto \\zeta({1\\over 2}+it)$. Moreover, we show that the curve $t\\mapsto (\\zeta({1\\over 2}+it),\\zeta'({1\\over 2}+it))$ is not dense in $C^2$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-26T12:24:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "arbitrarily large imaginary part",
      "heuristic interpretation",
      "simple roots",
      "complex number",
      "regularity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.5339G"
    }
  }
}