{
  "id": "0906.2132",
  "version": "v1",
  "published": "2009-06-11T15:13:10.000Z",
  "updated": "2009-06-11T15:13:10.000Z",
  "title": "Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions",
  "authors": [
    "Alessandro Languasco",
    "Alessandro Zaccagnini"
  ],
  "comment": "12 pages, 6 tables",
  "journal": "Experimental Mathematics 19 (2010), 279-284",
  "doi": "10.1080/10586458.2010.10390624",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give explicit numerical values with 100 decimal digits for the Mertens constant involved in the asymptotic formula for $\\sum\\limits_{\\substack{p\\leq x p\\equiv a \\bmod{q}}}1/p$ and, as a by-product, for the Meissel-Mertens constant defined as $\\sum_{p\\equiv a \\bmod{q}} (\\log(1-1/p)+1/p)$, for $q \\in \\{3$, ..., $100\\}$ and $(q, a) = 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-11T15:13:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11-04",
      "11Y60"
    ],
    "keywords": [
      "arithmetic progressions",
      "decimal digits",
      "asymptotic formula",
      "explicit numerical values",
      "by-product"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2132L"
    }
  }
}