{
  "id": "1206.3981",
  "version": "v1",
  "published": "2012-06-18T16:23:30.000Z",
  "updated": "2012-06-18T16:23:30.000Z",
  "title": "Ramanujan series upside-down",
  "authors": [
    "Jesús Guillera",
    "Mathew Rogers"
  ],
  "comment": "28 pages",
  "doi": "10.1017/S1446788714000147",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that there is a correspondence between Ramanujan-type formulas for 1/\\pi, and formulas for Dirichlet L-values. The same method also allows us to resolve certain values of the Epstein zeta function in terms of rapidly converging hypergeometric functions. The Epstein zeta functions were previously studied by Glasser and Zucker.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-18T16:23:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramanujan series upside-down",
      "epstein zeta function",
      "dirichlet l-values",
      "ramanujan-type formulas",
      "rapidly converging hypergeometric functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.3981G"
    }
  }
}