{
  "id": "1801.10184",
  "version": "v1",
  "published": "2018-01-30T19:40:42.000Z",
  "updated": "2018-01-30T19:40:42.000Z",
  "title": "On continued fraction expansions of quadratic irrationals in positive characteristic",
  "authors": [
    "Frédéric Paulin",
    "Uri Shapira"
  ],
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "Let $P$ be a prime polynomial in the variable $Y$ over a finite field and let $f$ be a quadratic irrational in the field of formal Laurant series in the variable $Y^{-1}$. We study the asymptotic properties of the degrees of the coefficients of the continued fraction expansion of quadratic irrationals such as $P^nf$ and prove results that are in sharp contrast to the analogue situation in zero characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-30T19:40:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continued fraction expansion",
      "quadratic irrational",
      "positive characteristic",
      "formal laurant series",
      "analogue situation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}