Math 254a: Zeta Functions and L-series
نویسنده
چکیده
Theorem 1.1. Let G be a group of Dirichlet characters modulo n, and KG the associated field. Fix a prime number p, and let H1 ⊂ H2 ⊂ G be the groups of χ such that χ(p) = 1 or χ(p) 6= 0 respectively. Then G/H2 ∼= IKG,p ⊂ Gal(KG/Q), and G/H1 ∼= DKG,p (note that these are non-canonical isomorphisms). We are now ready to prove the theorem on factoring Dedekind zeta functions of sub-cyclotomic fields in terms of Dirichlet L-series. Theorem 1.2. Given a number field K ⊂ Q(ζn), let GK be the corresponding group of Dirichlet characters modulo n. Then for s > 1 we have
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تاریخ انتشار 2005