Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On the $l$-adic Iwasawa $\lambda$-invariant in a $p$-extension
HTML articles powered by AMS MathViewer

by Eduardo Friedman and Jonathan W. Sands PDF
Math. Comp. 64 (1995), 1659-1674 Request permission


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.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 11R23, 11Y40
  • Retrieve articles in all journals with MSC: 11R23, 11Y40
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 1659-1674
  • MSC: Primary 11R23; Secondary 11Y40
  • DOI:
  • MathSciNet review: 1308453