\(\lambda\)-invariants and \(\Gamma\)-transforms
type: Item
instance of: scholarly article
title: \(\lambda\)-invariants and \(\Gamma\)-transforms
zbMATH Open document ID: 0689.12004
DOI: 10.1007/BF01165825
author: Nancy Childress
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155412
review text: 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.
reviewed by: Lawrence C. Washington
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11S80
zbMATH DE Number: 4128937
zbMATH Keywords: Iwasawa theory
zbMATH Keywords: \(p\)-adic analysis
zbMATH Keywords: \(p\)-adic measure
zbMATH Keywords: \(\Gamma\)-transform
zbMATH Keywords: \(\lambda\)-invariants
zbMATH Keywords: \(p\)-adic \(L\)-functions
MaRDI profile type: Publication
cites work: The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
cites work: On the Iwasawa Invariants of Totally Real Number Fields
cites work: On \(p\)-adic \(L\)-functions
cites work: Q4177670
cites work: Q3874309
cites work: On the \(\mu\)-invariant of the \(\Gamma\)-transform of a rational function
cites work: Q3943047
OpenAlex ID: W2913467923
description: scientific article; zbMATH DE number 4128937