{
  "id": "2111.01044",
  "version": "v2",
  "published": "2021-11-01T15:50:48.000Z",
  "updated": "2022-05-18T12:49:26.000Z",
  "title": "Improved Constants for Effective Irrationality Measures from Hypergeometric Functions",
  "authors": [
    "Paul Voutier"
  ],
  "comment": "Referee changes and other small corrections made",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "In this paper, we simplify and improve the constant, $c$, that appears in effective irrationality measures, $|(a/b)^{m/n}-p/q|>c|q|^{-(\\kappa+1)}$, obtained from the hypergeometric method for $a/b$ near $1$. The dependence of $c$ on $|a|$ in our result is best possible (as is the dependence on $n$ in many cases). For some applications, the dependence of this constant on $|a|$ becomes important. We also establish some new inequalities for hypergeometric functions that are useful in other diophantine settings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-05-18T12:49:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J82",
      "11J68",
      "33C05"
    ],
    "keywords": [
      "effective irrationality measures",
      "hypergeometric functions",
      "dependence",
      "diophantine settings",
      "hypergeometric method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}