Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Invariant, Modular Form, and Lattice Points   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 $\tau\to
N\in\mathbb{Z}$, is related to that of lattice points inside 4-dimensional
simplex, and we discuss a relationship with the irreducible representations of
the fundamental group.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin