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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the $l$-adic Iwasawa $\lambda$-invariant in a $p$-extension
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by Eduardo Friedman and Jonathan W. Sands PDF
Math. Comp. 64 (1995), 1659-1674 Request permission

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.
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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