{
  "id": "math/0202141",
  "version": "v2",
  "published": "2002-02-15T10:16:36.000Z",
  "updated": "2002-02-18T06:13:50.000Z",
  "title": "A strengthening of the Nyman-Beurling criterion for the Riemann Hypothesis",
  "authors": [
    "Luis Baez-Duarte"
  ],
  "comment": "7 pages, 3 typos corrected, one reference added",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\rho(x)=x-[x]$, $\\chi=\\chi_{(0,1)}$. In $L_2(0,\\infty)$ consider the subspace $\\B$ generated by $\\{\\rho_a | a \\geq 1\\}$ where $\\rho_a(x):=\\rho(\\frac{1}{ax})$. By the Nyman-Beurling criterion the Riemann hypothesis is equivalent to the statement $\\chi\\in\\bar{\\B}$. For some time it has been conjectured, and proved in this paper, that the Riemann hypothesis is equivalent to the stronger statement that $\\chi\\in\\bar{\\Bnat}$ where $\\Bnat$ is the much smaller subspace generated by $\\{\\rho_a | a\\in\\Nat\\}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-02-18T06:13:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann hypothesis",
      "nyman-beurling criterion",
      "equivalent",
      "strengthening"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2141B"
    }
  }
}