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We study the Iwasawa λ-invariant of the cyclotomic ℤ 2 -extension of Q(p) for an odd prime number p which satisfies p ≡ 1 (mod 16) relating it to units having certain properties. We give an upper bound of λ and show λ = 0 in certain cases. We also give new numerical examples of λ = 0.

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