Quantum Invariant, Modular Form, and Lattice Points
| dc.creator | Hikami, Kazuhiro | |
| dc.date | 2004-09-08 | |
| dc.date.accessioned | 2026-07-07T06:23:14Z | |
| dc.date.available | 2026-07-07T06:23:14Z | |
| dc.description | We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold with 4-singular fibers. We define the Eichler integrals of the modular forms with half-integral weight, and we show that the invariant is rewritten as a sum of the Eichler integrals. Using a nearly modular property of the Eichler integral, we give an exact asymptotic expansion of the WRT invariant in $N\to\infty$. We reveal that the number of dominating terms, which is the number of the non-vanishing Eichler integrals in a limit $τ\to N\in\mathbb{Z}$, is related to that of lattice points inside 4-dimensional simplex, and we discuss a relationship with the irreducible representations of the fundamental group. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0409016 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0409016 | |
| dc.identifier | IMRN 2005:3 (2005) 121--154 | |
| dc.identifier | doi:10.1155/IMRN.2005.121 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96163 | |
| dc.subject | Mathematical Physics | |
| dc.title | Quantum Invariant, Modular Form, and Lattice Points | |
| dc.type | text |