Quantum Invariants, Modular Forms, and Lattice Points II
量子代数
2010-03-11 v1 几何拓扑
摘要
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.
引用
@article{arxiv.math/0604091,
title = {Quantum Invariants, Modular Forms, and Lattice Points II},
author = {Kazuhiro Hikami},
journal= {arXiv preprint arXiv:math/0604091},
year = {2010}
}