Irreducibility of some orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
The 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.
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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...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2011
ISSN: 0019-3577
DOI: 10.1016/j.indag.2011.02.003