Quantum Knot Invariant for Torus Link and Modular Forms

Abstract

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.

24 pages

References in corpus (5)

• Mock Theta Functions
• A Link Invariant from Quantum Dilogarithm
• q-series and L-functions related to half-derivatives of the Andrews--Gordon identity
• Higher Order Terms in the Melvin-Morton Expansion of the Colored Jones Polynomial
• On the volume conjecture for hyperbolic knots

Cited by in corpus (18)

• Resurgence in complex Chern-Simons theory
• Torus Knot and Minimal Model
• On the Quantum Invariant for the Spherical Seifert Manifold
• On the Quantum Invariant for the Brieskorn Homology Spheres
• An introduction to the volume conjecture and its generalizations
• Higher depth quantum modular forms and plumbed $3$-manifolds
• Quantum Invariants, Modular Forms, and Lattice Points II
• A cabling formula for the colored Jones polynomial
• Congruent skein relations for colored HOMFLY-PT invariants and colored Jones polynomials
• Resurgence of the Kontsevich-Zagier power series
• $\hat{Z}$ invariants at rational $\tau$
• Resurgent Analysis for Some 3-manifold Invariants
• Asymptotics of the Colored Jones Polynomial and the A-Polynomial
• Superconformal Algebras and Mock Theta Functions
• Representations and the colored Jones polynomial of a torus knot
• Torus knot state asymptotics
• Colored Jones polynomials with polynomial growth
• Superconformal Algebras and Mock Theta Functions 2. Rademacher Expansion for K3 Surface