Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the $ l$-adic Iwasawa $ \lambda$-invariant in a $ p$-extension


Authors: Eduardo Friedman and Jonathan W. Sands
Journal: Math. Comp. 64 (1995), 1659-1674
MSC: Primary 11R23; Secondary 11Y40
MathSciNet review: 1308453
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For distinct primes l and p, the Iwasawa invariant $ \lambda _l^ - $ stabilizes in the cyclotomic $ {\mathbb{Z}_p}$-tower over a complex abelian base field. We calculate this stable invariant for $ p = 3$ and various l and K. Our motivation was to search for a formula of Riemann-Hurwitz type for $ \lambda _l^ - $ that might hold in a p-extension. From our numerical results, it is clear that no formula of such a simple kind can hold. In the course of our calculations, we develop a method of computing $ \lambda _l^ - $ for an arbitrary complex abelian field and, for $ p = 3$, we make effective Washington's theorem on the stabilization of the l-part of the class group in the cyclotomic $ {\mathbb{Z}_p}$-extension. A new proof of this theorem is given in the appendix.


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


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11R23, 11Y40

Retrieve articles in all journals with MSC: 11R23, 11Y40


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1995-1308453-8
PII: S 0025-5718(1995)1308453-8
Keywords: Relative class number, $ {\mathbb{Z}_l}$-extension, Iwasawa lambda invariant
Article copyright: © Copyright 1995 American Mathematical Society