{
  "id": "1702.01915",
  "version": "v1",
  "published": "2017-02-07T07:57:49.000Z",
  "updated": "2017-02-07T07:57:49.000Z",
  "title": "continued fraction expansions of algebraic numbers",
  "authors": [
    "Xianzu Lin"
  ],
  "comment": "21pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we establish properties of independence for the continued fraction expansions of two algebraic numbers. Roughly speaking, if the continued fraction expansions of two irrational algebraic numbers have the same long sub-word, then the two continued fraction expansions have the same tails. If the two expansions have mirror symmetry long sub-words, then both the two algebraic numbers are quadratic. Applying the above results, we prove a theorem analogous to the Roth's theorem about approximation by algebraic numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-07T07:57:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11J81"
    ],
    "keywords": [
      "continued fraction expansions",
      "mirror symmetry long sub-words",
      "irrational algebraic numbers",
      "roths theorem",
      "independence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}