Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Character theory approach to Sato-Tate groups   In this article, we propose to use the character theory of compact Lie groups
and their orthogonality relations for the study of Frobenius distribution and
Sato-Tate groups. The results show the advantages of this new approach in
several aspects. With samples of Frobenius ranging in size much smaller than
the moment statistic approach, we obtain very good approximation to the
expected values of these orthogonality relations, which give useful information
about the underlying Sato-Tate groups and strong evidence of the correctness of
the generalized Sato-Tate conjecture. In fact, $2^{10}$ to $2^{12}$ points
provide satisfactory convergence. Even for $g = 2$, the classical approach
using moment statistics requires about $2^{30}$ sample points to obtain such
information.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg