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See detailReductions of points on algebraic groups II
Bruin, Peter; Perucca, Antonella UL

in Glasgow Mathematical Journal (2020)

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See detailOn mod $p$ representations which are defined over $\Bbb F_p$: II
Kilford, L. J. P.; Wiese, Gabor UL

in Glasgow Mathematical Journal (2010), 52(2), 391--400

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 ... [more ▼]

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. [less ▲]

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