We study the SU(2) Witten-Reshetikhin-Turaev (WRT) invariant for the Seifert fibered homology spheres with -exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms with weight and . By use of nearly modular property of the Eichler integrals we shall obtain asymptotic expansions of the WRT invariant in the large- limit. We further reveal that the number of the gauge equivalent classes of flat connections, which dominate the asymptotics of the WRT invariant in , is related to the number of integral lattice points inside the -dimensional tetrahedron.
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2006
American Institute of Physics
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