Quantum Knot Invariant for Torus Link and Modular Forms

Details Quantum Knot Invariant for Torus Link and Modular Forms Quantum Knot Invariant for Torus Link and Modular Forms

2003-05-20

arxiv.org/abs/math-ph/0305039v2

Commun. Math. Phys. 246, 403-426 (2004)

Physics

Mathematical Physics

24 pages

Scientific paper

10.1007/s00220-004-1046-2

We consider an asymptotic expansion of Kashaev's invariant or the colored
Jones function for the torus link T(2,2m). We shall give q-series identity
related to these invariants, and show that the invariant is regarded as a limit
of q being N-th root of unity of the Eichler integral of the modular form of
weight 3/2.

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