Geodesic
ON MOD p REPRESENTATIONS WHICH ARE DEFINED OVER p: II
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 391-400

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DOI

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.
DOI : 10.1017/S001708951000008X
Mots-clés : Primary 11F33, secondary 11F25, 11R29 
KILFORD, L. J. P.; WIESE, GABOR. ON MOD p REPRESENTATIONS WHICH ARE DEFINED OVER p: II. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 391-400. doi: 10.1017/S001708951000008X
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     journal = {Glasgow mathematical journal},
     pages = {391--400},
     year = {2010},
     volume = {52},
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     doi = {10.1017/S001708951000008X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951000008X/}
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