Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

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


On small Iwasawa invariants and imaginary quadratic fields

Author: Jonathan W. Sands
Journal: Proc. Amer. Math. Soc. 112 (1991), 671-684
MSC: Primary 11R23
MathSciNet review: 1057961
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ p$ is an odd prime that does not divide the class number of the imaginary quadratic field $ k$, and the cyclotomic $ {\mathbb{Z}_p}$-extension of $ k$ has $ \lambda $-invariant less than or equal to two, we prove that every totally ramified $ {\mathbb{Z}_p}$-extension of $ k$ has $ \mu $-invariant equal to zero and $ \lambda $-invariant less than or equal to two. Combined with a result of Bloom and Gerth, this has the consequence that $ \mu = 0$ for every $ {\mathbb{Z}_p}$-extension of $ k$, under the same assumptions. In the principal case under consideration, Iwasawa's formula for the power of $ p$ in the class number of the $ n$th layer of a $ {\mathbb{Z}_p}$-extension becomes valid for all $ n$ , and is completely explicit.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11R23

Retrieve articles in all journals with MSC: 11R23

Additional Information

PII: S 0002-9939(1991)1057961-4
Keywords: Iwasawa invariant, distinguished polynomial, class field
Article copyright: © Copyright 1991 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia