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Quantum Invariants, Modular Forms, and Lattice Points II

Kazuhiro Hikami
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Abstract

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms with weight 1/2 and 3/2. By use of nearly modular property of the Eichler integrals we shall obtain asymptotic expansions of the WRT invariant in the large-N limit. We further reveal that the number of the gauge equivalent classes of flat connections, which dominate the asymptotics of the WRT invariant in N ->\infinity, is related to the number of integral lattice points inside the M-dimensional tetrahedron.

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Kazuhiro Hikami. 2006-04-05. Quantum Invariants, Modular Forms, and Lattice Points II. https://doi.org/10.1063/1.2349484

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