On mod p representations which are defined over F_p: II

Details On mod p representations which are defined over F_p: II On mod p representations which are defined over F_p: II

2009-05-27

arxiv.org/abs/0905.4372v1

Mathematics

Number Theory

10 pages

Scientific paper

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.

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