Artin's L-functions and one-dimensional characters

JOURNAL OF NUMBER THEORY

卷:124

Article

Nicolae, Florin

关键词: artin L-function;    M-group;    quasi-M-group;   

DOI  :  10.1016/j.jnt.2006.08.004

来源: Elsevier

【 摘 要 】

Let K/Q be a finite Galois extension with the Galois group G, let chi 1, ... , chi r be the irreducible non-trivial characters of G, and let A be the C-algebra generated by the Artin L-functions L (s, chi 1), ... , L (s, chi r). Let 5 be the subalgebra of A generated by the L-functions corresponding to induced characters of non-trivial one-dimensional characters of subgroups of G. We prove: (1) B is of Krull dimension r and has the same quotient field as A; (2) B = A iff G is M-group; (3) the integral closure of B in A equals A iff G is quasi-M-group. (C) 2006 Elsevier Inc. All rights reserved.

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