A heuristic irreducibility test for univariate polynomials
نویسندگان
چکیده
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.
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2000 AMS Subject Classification: Primary 12E05
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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: Journal of Symbolic Computation
سال: 1992
ISSN: 0747-7171
DOI: 10.1016/0747-7171(92)90005-o