{
  "id": "1608.06737",
  "version": "v1",
  "published": "2016-08-24T07:51:40.000Z",
  "updated": "2016-08-24T07:51:40.000Z",
  "title": "The Riemann Hypothesis: A Qualitative Characterization of the Nontrivial Zeros of the Riemann Zeta Function Using Polylogarithms",
  "authors": [
    "Lazhar Fekih-Ahmed"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We formulate a parametrized uniformly absolutely globally convergent series of $\\zeta$(s) denoted by Z(s, x). When expressed in closed form, it is given by Z(s, x) = (s -- 1)$\\zeta$(s) + 1 x Li s z z -- 1 dz, where Li s (x) is the polylogarithm function. As an immediate first application of the new parametrized series, a new expression of $\\zeta$(s) follows: (s -- 1)$\\zeta$(s) = -- 1 0 Li s z z -- 1 dz. As a second important application, using the functional equation and exploiting uniform convergence of the series defining Z(s, x), we have for any non-trivial zero s",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-24T07:51:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "riemann hypothesis",
      "nontrivial zeros",
      "qualitative characterization",
      "absolutely globally convergent series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}