{
  "id": "1609.06531",
  "version": "v1",
  "published": "2016-09-21T12:44:03.000Z",
  "updated": "2016-09-21T12:44:03.000Z",
  "title": "On the expansions of real numbers in two multiplicative dependent bases",
  "authors": [
    "Yann Bugeaud",
    "Dong Han Kim"
  ],
  "comment": "15pages. arXiv admin note: substantial text overlap with arXiv:1512.06935",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $r \\ge 2$ and $s \\ge 2$ be multiplicatively dependent integers. We establish a lower bound for the sum of the block complexities of the $r$-ary expansion and of the $s$-ary expansion of an irrational real number, viewed as infinite words on $\\{0, 1, \\ldots , r-1\\}$ and $\\{0, 1, \\ldots , s-1\\}$, and we show that this bound is best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-21T12:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "68R15"
    ],
    "keywords": [
      "multiplicative dependent bases",
      "ary expansion",
      "irrational real number",
      "block complexities",
      "multiplicatively dependent integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}