43 citations · 247 across the 8 of their papers we have counts for
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Mock (False) Theta Functions as Quantum Invariants
Kazuhiro Hikami
We show a correspondence between the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert manifold M(p,q,r) and Ramanujan's mock theta functions.
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…
Quantum Knot Invariant for Torus Link and Modular Forms
Kazuhiro Hikami
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, an…
Hyperbolic Structure Arising from a Knot Invariant
Kazuhiro Hikami
We study the knot invariant based on the quantum dilogarithm function. This invariant can be regarded as a non-compact analogue of Kashaev's invariant, or the colored Jones invaria…