{
  "id": "math/0404213",
  "version": "v2",
  "published": "2004-04-10T20:21:23.000Z",
  "updated": "2004-04-15T10:45:37.000Z",
  "title": "A sharpening of Li's criterion for the Riemann Hypothesis",
  "authors": [
    "André Voros"
  ],
  "comment": "1 Latex file, 5 pages, submitted to C.R. Acad. Sci. (Paris) S\\'er. I. V2: notation corrected in eq.(7); eq.(9) made more precise",
  "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. In particular, we argue that if (and only if) the Hypothesis is true, $\\lambda_n \\sim n(A \\log n +B)$ for $n \\to \\infty$ (with explicit $A>0$ and $B$). The approach also holds for more general zeta or $L$-functions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-04-15T10:45:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "30B40",
      "41A60"
    ],
    "keywords": [
      "lis criterion",
      "riemann hypothesis",
      "sharpening",
      "asymptotic formulae",
      "general zeta"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4213V"
    }
  }
}