Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenvalues of Hecke operators on Hilbert modular groups   We consider cuspidal representations in spaces of automorphic forms for the
congruence subgroup $\Gamma_0(I)$ of Hilbert modular groups for some number
field $F$. To each such representation are associated the eigenvalue
$\lambda_j$ of the Casimir operator at each real place $j$ of $F$, and the
number $\ld_{\mathfrak p}$ parametrizing the eigenvalue of the Hecke operator
$T_{\mathfrak p^2}$ at each finite place $\mathfrak p$ outside the ideal $I$.
We study the joint distribution of the $\lambda_j$ for all real places $j$, and
the $\ld_{\mathfrak p}$ for finitely many $\mathfrak p$ outside $I$, over the
cuspidal representations. This distribution is given by the product of the
Plancherel measure at each real place and the Sato-Tate measure at each finite
place.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ