\(\lambda\)-invariants and \(\Gamma\)-transforms
In his work on the vanishing of the Iwasawa \(\mu\)-invariant, \textit{W. Sinnott} [Invent. Math. 75, 273--282 (1984; Zbl 0531.12004)] showed (approximately) that, under certain conditions, the \(\mu\)-invariant of a \(p\)-adic measure equals the \(\mu\)-invariant of its \(\Gamma\)-transform. The purpose of the present paper is to investigate the relationship between the \(\lambda\)-invariants. Let \(p\) be an odd prime and let \(\alpha\) be a measure with values in the integers of a finite extension of \({\mathbb Q}_ p\). If the \(\lambda\)-invariant associated to the \(\Gamma\)-transform of \(\alpha\) is at most \(p\), then \(p\) times this invariant equals the \(\lambda\)-invariant of a measure closely associated to \(\alpha\). This is applied to the computation of \(\lambda\)-invariants of \(p\)-adic \(L\)-functions.
scientific article; zbMATH DE number 4128937