{
  "id": "1705.09918",
  "version": "v1",
  "published": "2017-05-28T09:40:13.000Z",
  "updated": "2017-05-28T09:40:13.000Z",
  "title": "A criterion related to the Riemann Hypothesis",
  "authors": [
    "Helmut Maier",
    "Michael Th. Rassias"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "A crucial role in the Nyman-Beurling-B\\'aez-Duarte approach to the Riemann Hypothesis is played by the distance \\[ d_N^2:=\\inf_{A_N}\\frac{1}{2\\pi}\\int_{-\\infty}^\\infty\\left|1-\\zeta A_N\\left(\\frac{1}{2}+it\\right)\\right|^2\\frac{dt}{\\frac{1}{4}+t^2}\\:, \\] where the infimum is over all Dirichlet polynomials $$A_N(s)=\\sum_{n=1}^{N}\\frac{a_n}{n^s}$$ of length $N$. In this paper we investigate $d_N^2$ under the assumption that the Riemann zeta function has four non-trivial zeros off the critical line. Thus we obtain a criterion for the non validity of the Riemann Hypothesis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-28T09:40:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C15",
      "11M26"
    ],
    "keywords": [
      "riemann hypothesis",
      "riemann zeta function",
      "nyman-beurling-baez-duarte approach",
      "dirichlet polynomials",
      "crucial role"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}