The zeros of Dedekind zeta functions and class numbers of CM-fields
نویسندگان
چکیده
Let F ′/F be a finite normal extension of number fields with Galois group Gal(F ′/F ). Let χ be an irreducible character of Gal(F ′/F ) of degree greater than one and L(s, χ) the associated Artin L-function. Assuming the truth of Artin’s conjecture, we have explicitly determined a zero-free region about 1 for L(s, χ). As an application we show that, for a CM-field K of degree 2n with solvable normal closure over Q, if n ≥ 370 as well as n / ∈ {384, 400, 416, 448, 512}, then the relative class number of K is greater than one.
منابع مشابه
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عنوان ژورنال:
- Math. Comput.
دوره 77 شماره
صفحات -
تاریخ انتشار 2008