Geodesic
The colored Jones polynomial of the figure-eight knot and a quantum modularity
Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 519-554

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DOI

We study the asymptotic behavior of the N-dimensional colored Jones polynomial of the figure-eight knot evaluated at $\exp \bigl ((u+2p\pi \sqrt {-1})/N\bigr )$, where u is a small real number and p is a positive integer. We show that it is asymptotically equivalent to the product of the p-dimensional colored Jones polynomial evaluated at $\exp \bigl (4N\pi ^2/(u+2p\pi \sqrt {-1})\bigr )$ and a term that grows exponentially with growth rate determined by the Chern–Simons invariant. This indicates a quantum modularity of the colored Jones polynomial.
DOI : 10.4153/S0008414X23000172
Mots-clés : Colored Jones polynomial, volume conjecture, figure-eight knot, Chern–Simons invariant, Reidemeister torsion, quantum modularity 
Murakami, Hitoshi. The colored Jones polynomial of the figure-eight knot and a quantum modularity. Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 519-554. doi: 10.4153/S0008414X23000172
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     title = {The colored {Jones} polynomial of the figure-eight knot and a quantum modularity},
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     year = {2024},
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