We study the SU(2) Witten-Reshetikhin-Turaev (WRT) 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 12 and 32. 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→∞, is related to the number of integral lattice points inside the M -dimensional tetrahedron.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics