Abstract
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.
| Original language | English |
|---|---|
| Article number | 102301 |
| Journal | Journal of Mathematical Physics |
| Volume | 47 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - Nov 8 2006 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
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Quantum invariants, modular forms, and lattice points II. / Hikami, Kazuhiro.
In: Journal of Mathematical Physics, Vol. 47, No. 10, 102301, 08.11.2006.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Quantum invariants, modular forms, and lattice points II
AU - Hikami, Kazuhiro
PY - 2006/11/8
Y1 - 2006/11/8
N2 - 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.
AB - 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.
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U2 - 10.1063/1.2349484
DO - 10.1063/1.2349484
M3 - Article
AN - SCOPUS:33750553391
VL - 47
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 10
M1 - 102301
ER -