The zeros of Dedekind zeta functions and class numbers of CM-fields
- Authors
- Lee, Geon-No; Kwon, Soun-Hi
- Issue Date
- 2008
- Publisher
- AMER MATHEMATICAL SOC
- Keywords
- CM-fields; class numbers; relative class numbers; Dedekind zeta functions
- Citation
- MATHEMATICS OF COMPUTATION, v.77, no.264, pp.2437 - 2445
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATICS OF COMPUTATION
- Volume
- 77
- Number
- 264
- Start Page
- 2437
- End Page
- 2445
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/125494
- DOI
- 10.1090/S0025-5718-08-02093-0
- ISSN
- 0025-5718
- Abstract
- Let F'/F be a finite normal extension of number fields with Galois group Gal(F'/F). Let. be an irreducible character of Gal(F'/F) of degree greater than one and L(s,chi) 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,.). 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 is not an element of {384, 400, 416, 448, 512}, then the relative class number of K is greater than one.
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