Analogues of Iwasawa's $\mu =0$ conjecture and the weak Leopoldt conjecture for a non-cyclotomic ${\mathbb{Z}}_2$-extension

Junhwa Choi, Yukako Kezuka, Yongxiong Li

Let $K=\mathbb{Q}(\sqrt{-q})$, where $q$ is any prime number congruent to $7$ modulo $8$, and let $\mathcal{O}$ be the ring of integers of $K$. The prime $2$ splits in $K$, say $…