Remote Access Mathematics of Computation
Green Open Access

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
DOI: https://doi.org/10.1090/S0025-5718-1995-1308453-8
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

Keywords: Relative class number, <!– MATH ${\mathbb {Z}_l}$ –> <IMG WIDTH="25" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\mathbb {Z}_l}$">-extension, Iwasawa lambda invariant
Article copyright: © Copyright 1995 American Mathematical Society