{
  "id": "1308.2720",
  "version": "v2",
  "published": "2013-08-12T23:50:12.000Z",
  "updated": "2016-05-13T21:01:44.000Z",
  "title": "Beukers-like proofs of irrationality for $ζ{(2)}$ and $ζ{(3)}$",
  "authors": [
    "F. M. S. Lima"
  ],
  "comment": "A few corrections in the text, equations are the same. 17 pages, no figures. Submitted (03/16/2016)",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this note, I develop step-by-step proofs of irrationality for $\\,\\zeta{(2)}\\,$ and $\\,\\zeta{(3)}$. Though the proofs follow closely those based upon unit square integrals proposed originally by Beukers, I introduce some modifications which certainly will be useful for those interested in understanding this kind of proof and/or trying to extend it to higher zeta values, Catalan's constant, or other related numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-12T23:50:12.000Z",
      "abstract": "In this note, I develop step-by-step proofs of irrationality for $\\,\\zeta{(2)}\\,$ and $\\,\\zeta{(3)}$. Though the proofs follow closely those based upon unit square integrals proposed originally by Beukers, I introduce some modifications which certainly will be useful for those interested in understanding this kind of proof and/or trying to extend it to higher zeta values or other related numbers.",
      "comment": "17 pages, no figures. Submitted (08/12/2013)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-05-13T21:01:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11J82",
      "11M06"
    ],
    "keywords": [
      "beukers-like proofs",
      "irrationality",
      "unit square integrals",
      "higher zeta values",
      "step-by-step proofs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2720L"
    }
  }
}