On the Iwasawa Invariants of $\mathbb Z_2$-Extensions of Certain Real Quadratic Fields

Abstract

For a real quadratic field $k$, we denote by $\lambda_2(k)$, $\mu_2(k)$ and $\nu_2(k)$ the Iwasawa $\lambda$-, $\mu$- and $\nu$-invariants of the cyclotomic $\mathbb Z_2$-extension of $k$, respectively. In this paper, we give certain families of real quadratic fields $k$ such that $\lambda_2(k)=\mu_2(k)=0$ and $\nu_2(k)=2$, by using Kuroda's class number formula.