{
  "id": "math/0512314",
  "version": "v1",
  "published": "2005-12-14T10:02:19.000Z",
  "updated": "2005-12-14T10:02:19.000Z",
  "title": "There are infinitely many limit points of the fractional parts of powers",
  "authors": [
    "ArtŪras Dubickas"
  ],
  "comment": "7 pages",
  "journal": "Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4, November 2005, pp. 391-397",
  "categories": [
    "math.NT"
  ],
  "abstract": "Suppose that $\\al>1$ is an algebraic number and $\\xi>0$ is a real number. We prove that the sequence of fractional parts $\\{\\xi \\al^n\\},$ $n =1,2,3,...,$ has infinitely many limit points except when $\\al$ is a PV-number and $\\xi \\in \\Q(\\al).$ For $\\xi=1$ and $\\al$ being a rational non-integer number, this result was proved by Vijayaraghavan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-14T10:02:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J71",
      "11R04",
      "11R06"
    ],
    "keywords": [
      "limit points",
      "fractional parts",
      "rational non-integer number",
      "algebraic number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}