{
  "id": "math/0611332",
  "version": "v2",
  "published": "2006-11-11T18:25:44.000Z",
  "updated": "2007-07-11T13:48:11.000Z",
  "title": "On Differences of Zeta Values",
  "authors": [
    "Philippe Flajolet",
    "Linas Vepstas"
  ],
  "comment": "18 pages",
  "doi": "10.1016/j.cam.2007.07.040",
  "categories": [
    "math.CA"
  ],
  "abstract": "Finite differences of values of the Riemann zeta function at the integers are explored. Such quantities, which occur as coefficients in Newton series representations, have surfaced in works of Maslanka, Coffey, Baez-Duarte, Voros and others. We apply the theory of Norlund-Rice integrals in conjunction with the saddle point method and derive precise asymptotic estimates. The method extends to Dirichlet L-functions and our estimates appear to be partly related to earlier investigations surrounding Li's criterion for the Riemann hypothesis.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-07-11T13:48:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "30B50",
      "39A05",
      "41A60"
    ],
    "keywords": [
      "zeta values",
      "differences",
      "earlier investigations surrounding lis criterion",
      "derive precise asymptotic estimates",
      "saddle point method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11332F"
    }
  }
}