{
  "id": "0802.1266",
  "version": "v1",
  "published": "2008-02-09T14:32:30.000Z",
  "updated": "2008-02-09T14:32:30.000Z",
  "title": "Rational approximations to $\\sqrt[3]{2}$ and other algebraic numbers revisited",
  "authors": [
    "P. M. Voutier"
  ],
  "comment": "published version, but with some small changes, including typo in statement of Lemma 5.1(b), leading to simpler proof of Theorem 2.1",
  "journal": "Journal de Th\\'eorie des Nombres de Bordeaux 19 (2007), 265-288",
  "doi": "10.5802/jtnb.586",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "In this paper, we establish improved effective irrationality measures for certain numbers of the form $\\sqrt[3]{n}$, using approximations obtained from hypergeometric functions. These results are very close to the best possible using this method. We are able to obtain these results by determining very precise arithmetic information about the denominators of the coefficients of these hypergeometric functions. Improved bounds for $\\theta(k,l;x)$ and $\\psi(k,l;x)$ for $k=1,3,4,6$ are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-09T14:32:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J68",
      "33C05"
    ],
    "keywords": [
      "algebraic numbers",
      "rational approximations",
      "hypergeometric functions",
      "precise arithmetic information",
      "effective irrationality measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.1266V"
    }
  }
}