{
  "id": "math/0604312",
  "version": "v1",
  "published": "2006-04-13T14:04:02.000Z",
  "updated": "2006-04-13T14:04:02.000Z",
  "title": "Irrationality of $ζ_q(1)$ and $ζ_q(2)$",
  "authors": [
    "Kelly Postelmans",
    "Walter Van Assche"
  ],
  "journal": "J. Number Theory 126 (2007), 119-154",
  "categories": [
    "math.CA",
    "math.NT"
  ],
  "abstract": "In this paper we show how one can obtain simultaneous rational approximants for $\\zeta_q(1)$ and $\\zeta_q(2)$ with a common denominator by means of Hermite-Pade approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, $\\zeta_q(1)$, $\\zeta_q(2)$ are linearly independent over the rationals. In particular this implies that $\\zeta_q(1)$ and $\\zeta_q(2)$ are irrational. Furthermore we give an upper bound for the measure of irrationality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-13T14:04:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11J82",
      "33D45"
    ],
    "keywords": [
      "irrationality",
      "multiple little q-jacobi polynomials",
      "common denominator",
      "upper bound",
      "simultaneous rational approximants"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4312P"
    }
  }
}