Reference : On mod $p$ representations which are defined over $\Bbb F_p$: II
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/11534
 Title : On mod $p$ representations which are defined over $\Bbb F_p$: II Language : English Author, co-author : Kilford, L. J. P. [> >] Wiese, Gabor [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : 2010 Journal title : Glasgow Mathematical Journal Volume : 52 Issue/season : 2 Pages : 391--400 Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 0017-0895 Abstract : [en] 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. Permalink : http://hdl.handle.net/10993/11534 DOI : 10.1017/S001708951000008X Commentary : 2610982 (2011m:11090)

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