Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Class numbers and Iwasawa invariants of quadratic fields

Author(s): 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: 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:

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