{
  "id": "math/0206176",
  "version": "v2",
  "published": "2002-06-18T14:30:19.000Z",
  "updated": "2002-06-21T05:48:33.000Z",
  "title": "Arithmetic of linear forms involving odd zeta values",
  "authors": [
    "Wadim Zudilin"
  ],
  "comment": "42 pages, LaTeX; slight modification of the absract",
  "journal": "J. Th\\'eorie Nombres Bordeaux 16:1 (2004), 251--291",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of $\\zeta(2)$ and $\\zeta(3)$, as well as to explain Rivoal's \"infinitely-many\" result (math.NT/0008051) and to prove that at least one of the four numbers $\\zeta(5)$, $\\zeta(7)$, $\\zeta(9)$, and $\\zeta(11)$ is irrational.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-06-21T05:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11J82",
      "33C60"
    ],
    "keywords": [
      "odd zeta values",
      "linear forms",
      "arithmetic",
      "general hypergeometric construction",
      "irrationality measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......6176Z"
    }
  }
}