{
  "id": "1512.06935",
  "version": "v1",
  "published": "2015-12-22T02:48:14.000Z",
  "updated": "2015-12-22T02:48:14.000Z",
  "title": "On the expansions of real numbers in two integer bases",
  "authors": [
    "Yann Bugeaud",
    "Dong Han Kim"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $r \\ge 2$ and $s \\ge 2$ be distinct integers. We establish that, if $r$ and $s$ are multiplicatively independent, then the $r$-ary expansion and the $s$-ary expansion of an irrational real number, viewed as infinite words on $\\{0, 1, \\ldots , r-1\\}$ and $\\{0, 1, \\ldots , s-1\\}$, respectively, cannot have simultaneously a low block complexity. In particular, they cannot be both Sturmian words. We also discuss the case where $r$ and $s$ are multiplicatively dependent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-22T02:48:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "68R15"
    ],
    "keywords": [
      "integer bases",
      "ary expansion",
      "irrational real number",
      "low block complexity",
      "infinite words"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151206935B"
    }
  }
}