Author:
KILFORD L. J. P.,WIESE GABOR
Abstract
AbstractThe behaviour of Hecke polynomials modulophas been the subject of some studies. In this paper we show that ifpis a prime, the set of integersNsuch that the Hecke polynomialsTN,χℓ,kfor all primes ℓ, all weightsk≥ 2 and all characters χ taking values in {±1} splits completely modulophas density 0, unconditionally forp= 2 and under the Cohen–Lenstra heuristics forp≥ 3. The method of proof is based on the construction of suitable dihedral modular forms.
Publisher
Cambridge University Press (CUP)