{
  "id": "2204.13887",
  "version": "v1",
  "published": "2022-04-29T05:24:54.000Z",
  "updated": "2022-04-29T05:24:54.000Z",
  "title": "The $a$-points of the Riemann zeta-function and the functional equation",
  "authors": [
    "Athanasios Sourmelidis",
    "Jörn Steuding",
    "Ade Irma Suriajaya"
  ],
  "comment": "Dedicated to the memory of Professor Eduard Wirsing, 12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\\zeta(s)=a$, where $a$ is an arbitrary fixed complex number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-29T05:24:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "functional equation",
      "riemann zeta-function",
      "arbitrary fixed complex number",
      "riemann hypothesis",
      "equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}