منابع مشابه
On the irreducibility of Hecke polynomials
Let Tn,k(X) be the characteristic polynomial of the nth Hecke operator acting on the space of cusp forms of weight k for the full modular group. We record a simple criterion which can be used to check the irreducibility of the polynomials Tn,k(X). Using this criterion with some machine computation, we show that if there exists n ≥ 2 such that Tn,k(X) is irreducible and has the full symmetric gr...
متن کاملIrreducibility of Hecke Polynomials
In this note, we show that if the characteristic polynomial of some Hecke operator Tn acting on the space of weight k cusp forms for the group SL2(Z ) is irreducible, then the same holds for Tp, where p runs through a density one set of primes. This proves that if Maeda’s conjecture is true for some Tn, then it is true for Tp for almost all primes p.
متن کاملThe irreducibility of some level 1 Hecke polynomials
Let Tp,k(x) be the characteristic polynomial of the Hecke operator Tp acting on the space of level 1 cusp forms Sk(1). We show that Tp,k(x) is irreducible and has full Galois group over Q for k ≤ 2000 and p < 2000, p prime.
متن کاملOn the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$
We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the repre...
متن کاملOn the Irreducibility of a Class of Polynomials, Iv
To the memory of Z. Z. Papp 1. Introduction. In this paper, we continue our investigations (cf. [5], [6], [9]) concerning reducibility of polynomials of the form g(f (x)) over Q, where g(x) is a monic irreducible polynomial in Z[x] and f (x) is a monic polynomial in Z[x] with distinct zeros in Q or, more generally, in a given algebraic number field K. We assume throughout this paper that the sp...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2008
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-08-02078-4