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On the Iwasawa $\lambda $-invariant of the cyclotomic $\mathbb {Z}_2$-extension of $\mathbb {Q}(\sqrt {p} )$
We study the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb {Z}_2$-extension of $\mathbb {Q}(\sqrt {p} )$ for an odd prime number $p$ which satisfies $p\equiv 1\pmod {16}$ relating it to units having certain properties. We give an upper bound of $\lambda$ and show $\lambda =0$ in certain cases. We also give …