Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Lower bounds for relative class numbers of CM-fields

Author: Stéphane Louboutin
Journal: Proc. Amer. Math. Soc. 120 (1994), 425-434
MSC: Primary 11R42; Secondary 11R29
MathSciNet review: 1169041
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {\mathbf{K}}$ be a CM-field that is a quadratic extension of a totally real number field $ {\mathbf{k}}$. Under a technical assumption, we show that the relative class number of $ {\mathbf{K}}$ is large compared with the absolute value of the discriminant of $ {\mathbf{K}}$, provided that the Dedekind zeta function of $ {\mathbf{k}}$ has a real zero $ s$ such that $ 0 < s < 1$. This result will enable us to get sharp upper bounds on conductors of totally imaginary abelian number fields with class number one or with prescribed ideal class groups.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11R42, 11R29

Retrieve articles in all journals with MSC: 11R42, 11R29

Additional Information

Keywords: Class number, CM-fields, zeta function
Article copyright: © Copyright 1994 American Mathematical Society