{
  "id": "math/0511674",
  "version": "v1",
  "published": "2005-11-28T12:48:53.000Z",
  "updated": "2005-11-28T12:48:53.000Z",
  "title": "On the complexity of algebraic number I. Expansions in integer bases",
  "authors": [
    "Boris Adamczewski",
    "Yann Bugeaud"
  ],
  "journal": "Ann. of Math. (2) 165 (2007), no. 2, 547--565",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $b \\ge 2$ be an integer. We prove that the $b$-adic expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-28T12:48:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J81",
      "11A63",
      "11B85",
      "68R15"
    ],
    "keywords": [
      "integer bases",
      "irrational algebraic number",
      "combinatorial transcendence criterion",
      "irrational morphic numbers",
      "irrational automatic numbers"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11674A"
    }
  }
}