Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
THE INDEX OF ELLIPTIC UNITS IN $\\boldsymbol{Z}_p$-EXTENSIONS, II
HASSAN OUKHABA
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2009 年 61 巻 2 号 p. 253-265

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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.
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© 2009 by THE TOHOKU UNIVERSITY
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