{
  "id": "1012.1709",
  "version": "v2",
  "published": "2010-12-08T09:17:47.000Z",
  "updated": "2012-11-23T09:37:30.000Z",
  "title": "Automatic continued fractions are transcendental or quadratic",
  "authors": [
    "Yann Bugeaud"
  ],
  "comment": "20 pages; the title has changed",
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish new combinatorial transcendence criteria for continued fraction expansions. Let $\\alpha = [0; a_1, a_2,...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients $(a_{\\ell})_{\\ell \\ge 1}$ of $\\alpha$ cannot be generated by a finite automaton, and that the complexity function of $(a_{\\ell})_{\\ell \\ge 1}$ cannot increase too slowly.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-23T09:37:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11J81",
      "11J87"
    ],
    "keywords": [
      "automatic continued fractions",
      "transcendental",
      "combinatorial transcendence criteria",
      "continued fraction expansions",
      "algebraic number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.1709B"
    }
  }
}