Tohoku Mathematical Journal
2009
June
SECOND SERIES VOL. 61, NO. 2

Tohoku Math. J.
61 (2009), 253-265

Title THE INDEX OF ELLIPTIC UNITS IN $\boldsymbol{Z}_p$-EXTENSIONS, II

Author Hassan Oukhaba

(Received September 25, 2007, revised December 15, 2008)
Abstract. In this paper we continue to explore the index of elliptic units. In a previous article we determined the asymptotic behavior in $\boldsymbol{Z}_p$-extensions of the $p$-part of this index divided by the $p$-part of the ideal class number. We proved the existence of an invariant $\mu_\infty$ which governs this behavior, and gave sufficient conditions for the vanishing of $\mu_\infty$. Here we give examples with nonzero $\mu_\infty$, especially in the case of anticyclotomic $\boldsymbol{Z}_p$-extensions.

2000 Mathematics Subject Classification. Primary 11G16; Secondary 11R23.

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