On the Iwasawa \(\lambda\)-invariants of imaginary quadratic fields
type: Item
instance of: scholarly article
title: On the Iwasawa \(\lambda\)-invariants of imaginary quadratic fields
zbMATH Open document ID: 0938.11051
author: Jangheon Oh
published in: Proceedings of the Japan Academy. Series A
publication date: 2000-06-12T00:00:00Z
review text: 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.
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 1335029
zbMATH Keywords: \(p\)-adic \(L\)-function
zbMATH Keywords: Iwasawa invariant
zbMATH Keywords: imaginary quadratic field
MaRDI profile type: Publication
full work available at URL: pjaa.75.29
OpenAlex ID: W2056775549
cites work: Computation of Iwasawa lambda invariants for imaginary quadratic fields
cites work: Q3726223
cites work: On the \(\mu\)-invariant of the \(\Gamma\)-transform of a rational function
cites work: Q3943047
DOI: 10.3792/PJAA.75.29
description: scientific article; zbMATH DE number 1335029