Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irreducibility and Galois group of Hecke polynomials   Let T_{n,k}(X) be the characteristic polynomial of the n-th Hecke operator
acting on the space of cusp forms of weight k for the full modular group. We
show that if there exists n>1 such that T_{n,k}(X) is irreducible and has the
full symmetric group as Galois group, then the same is true of T_{p,k}(X) for
all primes p.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int