{
  "id": "2311.06591",
  "version": "v1",
  "published": "2023-11-11T15:15:48.000Z",
  "updated": "2023-11-11T15:15:48.000Z",
  "title": "On Ramanujan's cubic continued fraction",
  "authors": [
    "Sushmanth J. Akkarapakam",
    "Patrick Morton"
  ],
  "comment": "40 pages, 1 Table",
  "categories": [
    "math.NT"
  ],
  "abstract": "The periodic points of the algebraic function defined by the equation $g(x,y) = x^3(4y^2+2y+1)-y(y^2-y+1)$ are shown to be expressible in terms of Ramanujan's cubic continued fraction $c(\\tau)$ with arguments in an imaginary quadratic field in which the prime $3$ splits. If $w = (a+\\sqrt{-d})/2$ lies in an order of conductor $f$ in $K$ and $9 \\mid N_{K/\\mathbb{Q}}(w)$, then one of these periodic points is $c(w/3)$, which is shown to generate the ring class field of conductor $2f$ over $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-11T15:15:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ramanujans cubic continued fraction",
      "periodic points",
      "imaginary quadratic field",
      "ring class field",
      "algebraic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}