On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{p})$ II

Abstract

In the preceding papers, we studied the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}(\sqrt{p})$ for an odd prime number $p$ using certain units and the invariants $n_0^{(r)}$ and $n_2$. In the present paper, we develop new criteria for Greenberg conjecture using $n_0^{(r)}$ and $n_2$.