{
  "id": "1208.3402",
  "version": "v1",
  "published": "2012-08-16T15:49:31.000Z",
  "updated": "2012-08-16T15:49:31.000Z",
  "title": "Partial quotients and representation of rational numbers",
  "authors": [
    "Jean Bourgain"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "It is shown that there is an absolute constant $C$ such that any rational $\\frac bq\\in]0, 1[, (b, q)=1$, admits a representation as a finite sum $\\frac bq=\\sum_\\alpha\\frac {b_\\alpha}{q_\\alpha}$ where $\\sum_\\alpha\\sum_ia_i(\\frac {b_\\alpha}{q_\\alpha})<C\\log q$ and $\\{a_i(x)\\}$ denotes the sequence of partial quotients of $x$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-16T15:49:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D68",
      "11A55"
    ],
    "keywords": [
      "partial quotients",
      "rational numbers",
      "representation",
      "finite sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.3402B"
    }
  }
}