{
  "id": "1004.1326",
  "version": "v1",
  "published": "2010-04-08T13:14:19.000Z",
  "updated": "2010-04-08T13:14:19.000Z",
  "title": "Approximation to points in the plane by SL(2,Z)-orbits",
  "authors": [
    "Michel Laurent",
    "Arnaldo Nogueira"
  ],
  "doi": "10.1112/jlms/jdr061",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let x be a point in R^2 with irrational slope and let \\Gamma denote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit \\Gamma x is dense in R^2. We give efective results on the approximation of a point y in R^2 by points of the form \\gamma x, where \\gamma belongs to \\Gamma, in terms of the size of \\gamma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-08T13:14:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximation",
      "irrational slope",
      "lattice sl",
      "efective results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1326L"
    }
  }
}