{
  "id": "1512.06511",
  "version": "v1",
  "published": "2015-12-21T07:42:51.000Z",
  "updated": "2015-12-21T07:42:51.000Z",
  "title": "Mahler's classification and a certain class of $p$-adic numbers",
  "authors": [
    "Tomohiro Ooto"
  ],
  "comment": "12 pages. arXiv admin note: text overlap with arXiv:1512.04041",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study a relation between digits of $p$-adic numbers and Mahler's classification. We show that an irrational $p$-adic number whose digits is automatic, primitive morphic, or Sturmian is an $S$-, $T$-, or $U_1$-number in the sense of Mahler's classification. Furthermore, we give an algebraic independence criterion for $p$-adic numbers whose digits are Sturmian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-21T07:42:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J61",
      "11J82",
      "11B85"
    ],
    "keywords": [
      "adic number",
      "mahlers classification",
      "algebraic independence criterion",
      "primitive morphic",
      "irrational"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151206511O"
    }
  }
}