{
  "id": "1710.04865",
  "version": "v1",
  "published": "2017-10-13T10:30:09.000Z",
  "updated": "2017-10-13T10:30:09.000Z",
  "title": "The colored Jones polynomial and Kontsevich-Zagier series for double twist knots",
  "authors": [
    "Jeremy Lovejoy",
    "Robert Osburn"
  ],
  "comment": "23 pages",
  "categories": [
    "math.GT",
    "math.CO",
    "math.NT"
  ],
  "abstract": "Using a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots $K_{(-m,-p)}$ and $K_{(-m,p)}$ where $m$ and $p$ are positive integers. In the $(-m,-p)$ case, this leads to new families of $q$-hypergeometric series generalizing the Kontsevich-Zagier series. Comparing with the cyclotomic expansion of the colored Jones polynomials of $K_{(m,p)}$ gives a generalization of a duality at roots of unity between the Kontsevich-Zagier function and the generating function for strongly unimodal sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-13T10:30:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "colored jones polynomial",
      "double twist knots",
      "kontsevich-zagier series",
      "cyclotomic expansion",
      "kontsevich-zagier function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}