{
  "id": "2307.13670",
  "version": "v1",
  "published": "2023-07-25T17:29:30.000Z",
  "updated": "2023-07-25T17:29:30.000Z",
  "title": "On the asymptotic expansions of various quantum invariants II: the colored Jones polynomial of twist knots at the root of unity $e^{\\frac{2π\\sqrt{-1}}{N+\\frac{1}{M}}}$ and $e^{\\frac{2π\\sqrt{-1}}{N}}$",
  "authors": [
    "Qingtao Chen",
    "Shengmao Zhu"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GT",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "This is the second article in a series devoted to the study of the asymptotic expansions of various quantum invariants related to the twist knots. In this article, following the method and results in \\cite{CZ23-1}, we present an asymptotic expansion formula for the colored Jones polynomial of twist knot $\\mathcal{K}_p$ with $p\\geq 6$ at the root of unity $e^{\\frac{2\\pi\\sqrt{-1}}{N+\\frac{1}{M}}}$ with $M\\geq 2$. Furthermore, by taking the limit $M\\rightarrow +\\infty$, we obtain an asymptotic expansion formula for the colored Jones polynomial of twist knots $\\mathcal{K}_p$ with $p\\geq 6$ at the root of unity $e^{\\frac{2\\pi\\sqrt{-1}}{N}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-25T17:29:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "colored jones polynomial",
      "twist knot",
      "quantum invariants",
      "asymptotic expansion formula",
      "second article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}