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ON MOD p REPRESENTATIONS WHICH ARE DEFINED OVER p: II

Published online by Cambridge University Press:  29 March 2010

L. J. P. KILFORD  and
GABOR WIESE
L. J. P. KILFORD
Affiliation:
Department of Mathematics, University Walk, Bristol BS8 1TW, United Kingdom E-mail: l.kilford@gmail.com Web page: http://www.maths.bris.ac.uk/~maljpk/
GABOR WIESE
Affiliation:
Universität Duisburg-Essen, Institut für Experimentelle Mathematik, Ellernstraße 29, 45326 Essen, Germany E-mail: gabor.wiese@uni-due.de Web page: http://maths.pratum.net/
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Abstract

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The behaviour of Hecke polynomials modulo p has been the subject of some studies. In this paper we show that if p is a prime, the set of integers N such that the Hecke polynomials TN,χℓ,k for all primes ℓ, all weights k ≥ 2 and all characters χ taking values in {±1} splits completely modulo p has density 0, unconditionally for p = 2 and under the Cohen–Lenstra heuristics for p ≥ 3. The method of proof is based on the construction of suitable dihedral modular forms.

Keywords

Primary 11F33secondary 11F2511R29
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 391 - 400
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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