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...

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Bibliographic Details
Published in:arXiv.org 2020-05
Main Author: Bengoechea, Paloma
Format: Article
Language:English
Subjects:
Polynomials
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Summary: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.
ISSN:2331-8422