{
  "id": "math/0310383",
  "version": "v2",
  "published": "2003-10-24T00:24:04.000Z",
  "updated": "2006-02-28T21:56:03.000Z",
  "title": "Continued Fractions with Partial Quotients Bounded in Average",
  "authors": [
    "Joshua N. Cooper"
  ],
  "comment": "7 pages, 0 figures; minor changes, to appear in Fibonacci Quarterly",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We ask, for which $n$ does there exists a $k$, $1 \\leq k < n$ and $(k,n)=1$, so that $k/n$ has a continued fraction whose partial quotients are bounded in average by a constant $B$? This question is intimately connected with several other well-known problems, and we provide a lower bound in the case of B=2.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-28T21:56:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K50",
      "11K38"
    ],
    "keywords": [
      "partial quotients",
      "continued fraction",
      "well-known problems",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10383C"
    }
  }
}