{
  "id": "1902.04746",
  "version": "v1",
  "published": "2019-02-07T13:46:47.000Z",
  "updated": "2019-02-07T13:46:47.000Z",
  "title": "An analytic approach to the Riemann hypothesis",
  "authors": [
    "Paolo D'Isanto",
    "Giampiero Esposito"
  ],
  "comment": "28 pages, 2 figures",
  "categories": [
    "math.CV"
  ],
  "abstract": "In this work we consider a new functional equation for the Riemann zeta-function in the critical half-strip. With the help of this equation we prove that finding non-trivial zeros of the Riemann zeta-function outside the critical line would be equivalent to the existence of complex numbers for which equation (5.1) in the paper holds. Such a condition is studied, and the attempt of proving the Riemann hypothesis is found to involve also the functional equation (6.26), where t is a real variable bigger than or equal to 1 and n is any natural number. The limiting behavior of the solutions as t approaches 1 is then studied in detail.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-07T13:46:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06"
    ],
    "keywords": [
      "riemann hypothesis",
      "analytic approach",
      "functional equation",
      "riemann zeta-function outside",
      "complex numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}