ANOTHER LOOK AT IWASAWA λ-INVARIANTS OF p-ADIC MEASURES ON $\mathbb {Z}_{p}^n$ AND Γ-TRANSFORMS

Abstract

In [Iwasawa λ-invariants of p-adic measures on [Formula: see text] and their Γ-transforms, J. Number Theory132(10) (2012) 2258–2266; Iwasawa λ-invariants and Γ-transforms of p-adic measure on [Formula: see text], Int. J. Number Theory6(8) (2010) 1819–1829], the author and Saikia defined Iwasawa λ-invariants for multi-variable power series and proved a relation between the Iwasawa λ-invariant of a p-adic measure on [Formula: see text] and its Γ-transform. In this paper, we give two new definitions of λ-invariants for multi-variable power series which generalize the λ-invariant of single variable power series and prove that the new λ-invariants also satisfy the same relation. We also give algebraic interpretations of the new λ-invariants and discuss an application of our main results.