Quantum Invariants, Modular Forms, and Lattice Points II

Details Quantum Invariants, Modular Forms, and Lattice Points II Quantum Invariants, Modular Forms, and Lattice Points II

2006-04-05

arxiv.org/abs/math/0604091v1

J. Math. Phys. 47, 102301-32pages (2006)

Mathematics

Quantum Algebra

Scientific paper

10.1063/1.2349484

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.

Affiliated with

Also associated with

No associations

Rating

Quantum Invariants, Modular Forms, and Lattice Points II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Invariants, Modular Forms, and Lattice Points II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Invariants, Modular Forms, and Lattice Points II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-418748