{
  "id": "0901.1637",
  "version": "v2",
  "published": "2009-01-12T18:44:39.000Z",
  "updated": "2015-02-05T22:40:53.000Z",
  "title": "Thue's Fundamentaltheorem, II: Further Refinements and Examples",
  "authors": [
    "Paul Voutier"
  ],
  "comment": "submitted version",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we sharpen and simplify our earlier results based on Thue's Fundamentaltheorem and use it to obtain effective irrationality measures for certain roots of polynomials of the form $(x-\\sqrt{t})^{n}+(x+\\sqrt{t})^{n}$, where $n \\geq 4$ is a positive integer and $t$ is a negative integer. For $n=4$ and $n=5$, we find infinitely many such algebraic numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-12T18:44:39.000Z",
      "title": "Thue's Fundamentaltheorem, II: Some New Irrationality Measures",
      "abstract": "In this paper, we apply Thue's Fundamentaltheorem to obtain effective irrationality measures for certain roots of particular polynomials of the form $(x-\\sqrt{t})^{n}+(x+\\sqrt{t})^{n}$, where $n \\geq 4$ is a positive integer and $t$ is a negative integer. For $n=4$ and $n=5$, we find infinitely many such numbers.",
      "comment": "The proofs in this version contain all the gory details",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-05T22:40:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J82",
      "11J68"
    ],
    "keywords": [
      "apply thues fundamentaltheorem",
      "effective irrationality measures",
      "polynomials",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}