Kummer generators and lambda invariants

Let be an imaginary quadratic field with 3∤d and let . Let ε0 be the fundamental unit of K0 and let λ be the Iwasawa λ-invariant for the cyclotomic Z3-extension of F0. The theory of 3-adic L-functions gives conditions for λ⩾2 in terms of ϵ0 and the class numbers of F0 and K0. We construct units of K1, the first level of the Z3-extension of K0, that potentially occur as Kummer generators of unramified extensions of F1(ζ3) and which give an algebraic interpretation of the condition that λ⩾2. We also discuss similar results on λ⩾2 that arise from work of Gross–Koblitz.