On mod p representations which are defined over F_p: II
Number Theory
2009-05-28 v1
Abstract
The behaviour of Hecke polynomials modulo p has been the subject of some study. In this note we show that, if p is a prime, the set of integers N such that the Hecke polynomials T^{N,\chi}_{l,k} for all primes l, all weights k>1 and all characters \chi taking values in {+1,-1} splits completely modulo p has density 0, unconditionally for p=2 and under the Cohen-Lenstra heuristics for odd p. The method of proof is based on the construction of suitable dihedral modular forms.
Cite
@article{arxiv.0905.4372,
title = {On mod p representations which are defined over F_p: II},
author = {L. J. P. Kilford and Gabor Wiese},
journal= {arXiv preprint arXiv:0905.4372},
year = {2009}
}
Comments
10 pages