On the $l$-adic Iwasawa $\lambda$-invariant in a $p$-extension
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- by Eduardo Friedman and Jonathan W. Sands PDF
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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
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Additional Information
- © Copyright 1995 American Mathematical Society
- 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