![]() ; Perucca, Antonella ![]() in Glasgow Mathematical Journal (2020) Detailed reference viewed: 35 (3 UL)![]() ; Wiese, Gabor ![]() 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 ▲] Detailed reference viewed: 49 (0 UL) |
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