{
  "id": "math/0211075",
  "version": "v4",
  "published": "2002-11-05T03:25:31.000Z",
  "updated": "2009-04-29T15:34:52.000Z",
  "title": "A Hypergeometric Approach, Via Linear Forms Involving Logarithms, to Irrationality Criteria for Euler's Constant",
  "authors": [
    "Jonathan Sondow",
    "Sergey Zlobin"
  ],
  "comment": "Typos in statement of Lemma 2 corrected, reference [3] updated, published version. Appendix by Sergey Zlobin",
  "journal": "Math. Slovaca 59 (2009), No. 3, 1-8",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "Using an integral of a hypergeometric function, we give necessary and sufficient conditions for irrationality of Euler's constant $\\gamma$. The proof is by reduction to known irrationality criteria for $\\gamma$ involving a Beukers-type double integral. We show that the hypergeometric and double integrals are equal by evaluating them. To do this, we introduce a construction of linear forms in 1, $\\gamma$, and logarithms from Nesterenko-type series of rational functions. In the Appendix, Sergey Zlobin gives a change-of-variables proof that the series and the double integral are equal.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-04-29T15:34:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11J86",
      "33C20"
    ],
    "keywords": [
      "irrationality criteria",
      "linear forms",
      "eulers constant",
      "hypergeometric approach",
      "logarithms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11075S"
    }
  }
}