Irreducibility and Galois group of Hecke polynomials
Number Theory
2020-06-01 v4
Abstract
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.
Cite
@article{arxiv.1703.02840,
title = {Irreducibility and Galois group of Hecke polynomials},
author = {Paloma Bengoechea},
journal= {arXiv preprint arXiv:1703.02840},
year = {2020}
}
Comments
There is an error in section 3, in using Theorem 3.2: the function f_{k,Dp^2,d} is not an eigenform a priori