{
  "id": "1709.07187",
  "version": "v1",
  "published": "2017-09-21T07:33:55.000Z",
  "updated": "2017-09-21T07:33:55.000Z",
  "title": "On convergence rate in the Gauss-Kuzmin problem for $θ$-expansions",
  "authors": [
    "Gabriela Ileana Sebe",
    "Dan Lascu"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "After providing an overview of $\\theta$-expansions introduced by Chakraborty and Rao, we focus on the Gauss-Kuzmin problem for this new transformation. Actually, we complete our study on these expansions by proving a two-dimensional Gauss-Kuzmin theorem. More exactly, we obtain such a theorem related to the natural extension of the associated measure-dynamical system. Finally, we derive explicit lower and upper bounds of the error term which provide interesting numerical calculations for the convergence rate involved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-21T07:33:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11K50",
      "28D05"
    ],
    "keywords": [
      "gauss-kuzmin problem",
      "convergence rate",
      "expansions",
      "two-dimensional gauss-kuzmin theorem",
      "error term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}