{
  "id": "0711.1753",
  "version": "v1",
  "published": "2007-11-12T11:41:25.000Z",
  "updated": "2007-11-12T11:41:25.000Z",
  "title": "On small fractional parts of polynomials",
  "authors": [
    "Nikolay G. Moshchevitin"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that for any real polynomial $f(x) \\in\\mathbb{R} [x]$ the set $$ \\{\\alpha \\in \\mathbb{R}: \\liminf_{n\\to \\infty} n\\log n ||\\alpha f(n)|| >0\\} $$ has positive Hausdorff dimension. Here $||\\xi ||$ means the distance from $\\xi $ to the nearest integer. Our result is based on an original method due to Y. Peres and W. Schlag.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-12T11:41:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J54"
    ],
    "keywords": [
      "small fractional parts",
      "real polynomial",
      "nearest integer",
      "original method",
      "positive hausdorff dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1753M"
    }
  }
}