On the irreducibility of Hecke polynomials
نویسنده
چکیده
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 group as Galois group, then the same is true of Tp,k(X) for each prime p ≤ 4, 000, 000.
منابع مشابه
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ورودعنوان ژورنال:
- Math. Comput.
دوره 77 شماره
صفحات -
تاریخ انتشار 2008