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arXiv · 0905.4372

On mod p representations which are defined over F_p: II

L. J. P. Kilford·Gabor Wiese
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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,χ}_{l,k} for all primes l, all weights k>1 and all characters χtaking 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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BibTeXRIS

L. J. P. Kilford, Gabor Wiese. 2009-05-27. On mod p representations which are defined over F_p: II. https://arxiv.org/abs/0905.4372

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