{
  "id": "1903.05060",
  "version": "v1",
  "published": "2019-03-12T17:09:37.000Z",
  "updated": "2019-03-12T17:09:37.000Z",
  "title": "The colored Jones polynomial and Kontsevich-Zagier series for double twist knots, II",
  "authors": [
    "Jeremy Lovejoy",
    "Robert Osburn"
  ],
  "comment": "30 pages",
  "categories": [
    "math.GT",
    "math.CO",
    "math.NT",
    "math.QA"
  ],
  "abstract": "Let $K_{(m,p)}$ denote the family of double twist knots where $2m-1$ and $2p$ are non-zero integers denoting the number of half-twists in each region. Using a result of Takata, we prove a formula for the colored Jones polynomial of $K_{(-m,-p)}$ and $K_{(-m,p)}$. The latter case leads to new families of $q$-hypergeometric series generalizing the Kontsevich-Zagier series. We also use Bailey pairs and formulas of Walsh to find cyclotomic-like expansions for the colored Jones polynomials of $K_{(m,p)}$ and $K_{(m,-p)}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-12T17:09:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D15",
      "57M27"
    ],
    "keywords": [
      "colored jones polynomial",
      "double twist knots",
      "kontsevich-zagier series",
      "non-zero integers",
      "hypergeometric series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}