Class number behavior in a two-tiered tower of ${\mathbb{Z}}_p$-extensions

Tsuyoshi Itoh

Let $k_{\infty }$ be the cyclotomic ${\mathbb{Z}}_p$-extension field of an algebraic number field $k$. Moreover, we take a ${\mathbb{Z}}_p$-extension $K_{\infty }$ over $k_{\infty }$. In this p…