{
  "id": "1812.10873",
  "version": "v1",
  "published": "2018-12-28T02:49:58.000Z",
  "updated": "2018-12-28T02:49:58.000Z",
  "title": "On the Divergence in the General Sense of $q$-Continued Fraction on the Unit Circle",
  "authors": [
    "Douglas Bowman",
    "James Mc Laughlin"
  ],
  "comment": "25 pages",
  "journal": "Communications in the Analytic Theory of Continued Fractions 11(2003), 25--49",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show, for each $q$-continued fraction $G(q)$ in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which $G(q)$ diverges in the general sense. This class includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fraction. We discuss the implications of our theorems for the general convergence of other $q$-continued fractions, for example the G\\\"{o}llnitz-Gordon continued fraction, on the unit circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-28T02:49:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A55"
    ],
    "keywords": [
      "unit circle",
      "general sense",
      "divergence",
      "rogers-ramanujan continued fraction",
      "ramanujan-selberg continued fraction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}