43 citations · 247 across the 8 of their papers we have counts for
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Quantum Invariant, Modular Form, and Lattice Points
Kazuhiro Hikami
We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold with 4-singular fibers. We define the Eichler integrals of the modular forms with half-integral we…
Hypergeometric Generating Function of L-function, Slater's Identities, and Quantum Invariant
Kazuhiro Hikami, Anatol N. Kirillov
We study certain connections between the quantum invariants of the torus knots T_{3,2^k} and some q-series identities. In particular, we obtain new generalizations of Slater's iden…
On the Quantum Invariant for the Brieskorn Homology Spheres
Kazuhiro Hikami
We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev invariant for the Brieskorn homology spheres by use of properties of the modular form follow…
Difference equation of the colored Jones polynomial for torus knot
Kazuhiro Hikami
We prove that the N-colored Jones polynomial for the torus knot T_{s,t} satisfies the second order difference equation, which reduces to the first order difference equation for a c…