{
  "id": "1501.04714",
  "version": "v1",
  "published": "2015-01-20T05:42:57.000Z",
  "updated": "2015-01-20T05:42:57.000Z",
  "title": "On Kurzweil's 0-1 Law in Inhomogeneous Diophantine Approximation",
  "authors": [
    "Michael Fuchs",
    "Dong Han Kim"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a sufficient and necessary condition such that for almost all $s\\in{\\mathbb R}$ \\[ \\|n\\theta-s\\|<\\psi(n)\\qquad\\text{for infinitely many}\\ n\\in{\\mathbb N}, \\] where $\\theta$ is fixed and $\\psi(n)$ is a positive, non-increasing sequence. This improves upon an old result of Kurzweil and contains several previous results as special cases: two theorems of Kurzweil, a theorem of Tseng and a recent result of the second author. Moreover, we also discuss an analogue of our result in the field of formal Laurent series which has similar consequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-20T05:42:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J83",
      "11K60",
      "37E10"
    ],
    "keywords": [
      "inhomogeneous diophantine approximation",
      "formal laurent series",
      "old result",
      "necessary condition",
      "special cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150104714F"
    }
  }
}