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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Class numbers and Iwasawa invariants
of quadratic fields


Author: James S. Kraft
Journal: Proc. Amer. Math. Soc. 124 (1996), 31-34
MSC (1991): Primary 11R11, 11R23, 11R29
MathSciNet review: 1301510
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\mathbf{Q}(\sqrt {-d}\hskip 2pt)$ and $\mathbf{Q}(\sqrt {3d}\hskip 2pt)$ be quadratic fields with $d \equiv $ 2 (mod 3) a positive integer. Let $\lambda ^-, \lambda ^+$ be the respective Iwasawa $\lambda $-invariants of the cyclotomic $\mathbf{Z}_3$-extension of these fields. We show that if $\lambda ^- =1$, then 3 does not divide the class number of $\mathbf{Q}(\sqrt {3d}\hskip 2pt)$ and $\lambda ^+ = 0$.


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

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Additional Information

James S. Kraft
Email: kraft@ithaca.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03085-7
PII: S 0002-9939(96)03085-7
Received by editor(s): September 1, 1993
Received by editor(s) in revised form: August 1, 1994
Communicated by: William Adams
Article copyright: © Copyright 1996 American Mathematical Society