{
  "id": "math/0506326",
  "version": "v2",
  "published": "2005-06-16T11:17:55.000Z",
  "updated": "2006-01-25T10:01:05.000Z",
  "title": "Sharpenings of Li's criterion for the Riemann Hypothesis",
  "authors": [
    "André Voros"
  ],
  "comment": "10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text corrections and updated references",
  "journal": "Math. Phys. Anal. Geom. 9 (2006) 53-63",
  "doi": "10.1007/s11040-005-9002-8",
  "categories": [
    "math.NT",
    "math.CV"
  ],
  "abstract": "Exact and asymptotic formulae are displayed for the coefficients $\\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \\to \\infty$ we obtain that if (and only if) the Hypothesis is true, $\\lambda_n \\sim n(A \\log n +B)$ (with $A>0$ and $B$ explicitly given, also for the case of more general zeta or $L$-functions); whereas in the opposite case, $\\lambda_n$ has a non-tempered oscillatory form.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-01-25T10:01:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "30B40",
      "41A60"
    ],
    "keywords": [
      "riemann hypothesis",
      "lis criterion",
      "sharpenings",
      "general zeta",
      "opposite case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}