Factoring Hecke polynomials modulo a prime
Number Theory
2016-09-07 v1
Abstract
Let T^{N,chi}_{p,k}(x) be the characteristic polynomial of the Hecke operator T_p acting on the space of cusp forms S_k(N,chi). We describe the factorization of T^{N,chi}_{p,k}(x) mod l as k varies, and we explicitly calculate those factorizations for N=1 and small l. These factorizations are used to deduce the irreducibility of certain T^{1,1}_{q,k}(x) from the irreducibility of T^{1,1}_{2,k}(x).
Cite
@article{arxiv.math/9811179,
title = {Factoring Hecke polynomials modulo a prime},
author = {J. Brian Conrey and David W. Farmer and Peter Jake Wallace},
journal= {arXiv preprint arXiv:math/9811179},
year = {2016}
}