منابع مشابه
Irreducibility 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 کاملOn 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 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.
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In the paper, we prove that the quotient of the polynomial representation of the double affine Hecke algebra (DAHA) by the radical of the duality pairing is always irreducible assuming that it is finite dimensional, which is always the case at roots of unity. We also find necessary and sufficient conditions for the radical to be zero, a q-generalization of Opdam’s formula for the singular k-par...
متن کاملIrreducibility testing of lacunary 0, 1-polynomials
A reciprocal polynomial g(x) ∈ Z[x] is such that g(0) 6= 0 and if g(α) = 0 then g(1/α) = 0. The non-reciprocal part of a monic polynomial f(x) ∈ Z[x] is f(x) divided by the product of its irreducible monic reciprocal factors (to their multiplicity). This paper presents an algorithm for testing the irreducibility of the nonreciprocal part of a 0, 1-polynomial (a polynomial having each coefficien...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2003
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2003.v10.n5.a13