On the Iwasawa \(\lambda\)-invariants of imaginary quadratic fields
Let \(p\) be an odd prime and \(k\) a complex quadratic number field, and let \(\lambda_p(k)\) denote Iwasawa's lambda-invariant of the cyclotomic \(\mathbb Z_p\)-extension of \(k\). Using an expression for the \(p\)-adic \(L\)-function due to \textit{W. Sinnott} [Invent. Math. 75, 273-282 (1984; Zbl 0531.12004)], the author reduces the computation of \(\lambda_p(k)\) to finding the first coefficient of the power series expansion of \(Q(T)\) not divisible by \(p\), where \(Q(T)\) is some explicitly given rational function of \(T\). Some worked examples are given.
scientific article; zbMATH DE number 1335029