{
  "id": "2101.08989",
  "version": "v1",
  "published": "2021-01-22T08:10:16.000Z",
  "updated": "2021-01-22T08:10:16.000Z",
  "title": "Fractional parts of powers of real algebraic numbers",
  "authors": [
    "Yann Bugeaud"
  ],
  "comment": "8 pages; comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\alpha$ be a real number greater than $1$. We establish an effective lower bound for the distance between an integral power of $\\alpha$ and its nearest integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-22T08:10:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J68",
      "11J86",
      "11R06"
    ],
    "keywords": [
      "real algebraic numbers",
      "fractional parts",
      "real number greater",
      "effective lower bound",
      "integral power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}