{
  "id": "1305.0035",
  "version": "v1",
  "published": "2013-04-30T21:56:58.000Z",
  "updated": "2013-04-30T21:56:58.000Z",
  "title": "Computing the residue of the Dedekind zeta function",
  "authors": [
    "Karim Belabas",
    "Eduardo Friedman"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Assuming the Generalized Riemann Hypothesis, Bach has shown that one can calculate the residue of the Dedekind zeta function of a number field K by a clever use of the splitting of primes p < X, with an error asymptotically bounded by 8.33 log D_K/(\\sqrt{X}\\log X), where D_K is the absolute value of the discriminant of K. Guided by Weil's explicit formula and still assuming GRH, we make a different use of the splitting of primes and thereby improve Bach's constant to 2.33. This results in substantial speeding of one part of Buchmann's class group algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-30T21:56:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R42",
      "11Y40"
    ],
    "keywords": [
      "dedekind zeta function",
      "buchmanns class group algorithm",
      "weils explicit formula",
      "absolute value",
      "generalized riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.0035B"
    }
  }
}