The index of elliptic units in $\boldsymbol{Z}_p$-extensions, II

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.