{
  "id": "1804.09922",
  "version": "v1",
  "published": "2018-04-26T07:40:15.000Z",
  "updated": "2018-04-26T07:40:15.000Z",
  "title": "Arithmetic of Catalan's constant and its relatives",
  "authors": [
    "Wadim Zudilin"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT",
    "math.CA",
    "math.CO"
  ],
  "abstract": "We prove that at least one of the six numbers $\\beta(2i)$ for $i=1,\\dots,6$ is irrational. Here $\\beta(s)=\\sum_{k=0}^\\infty(-1)^k(2k+1)^{-s}$ denotes Dirichlet's beta function, so that $\\beta(2)$ is Catalan's constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-26T07:40:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11Y60",
      "33C20"
    ],
    "keywords": [
      "catalans constant",
      "arithmetic",
      "denotes dirichlets beta function",
      "irrational"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}