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On the Quantum Invariant for the Spherical Seifert Manifold
We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert
manifold where is a finite subgroup of SU(2). We show
that the WRT invariants can be written in terms of the Eichler integral of the
modular forms with half-integral weight, and we give an exact asymptotic
expansion of the invariants by use of the nearly modular property of the
Eichler integral. We further discuss that those modular forms have a direct
connection with the polyhedral group by showing that the invariant polynomials
of modular forms satisfy the polyhedral equations associated to .Comment: 36 page