Rational Coates-Wiles series
type: Item
instance of: scholarly article
title: Rational Coates-Wiles series
zbMATH Open document ID: 0538.12003
author: Robert Gold
published in: Illinois Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: This article studies Coates-Wiles (CW) series and establishes a relationship between these series and the Iwasawa invariant \(\lambda^+\) of the \({\mathbb{Z}}_ p\)-extension of the maximum real subfield of the p-th cyclotomic field. The first part of the paper gives a simple characterization of rational CW series as a finite product of linear terms, by describing their roots and poles. It is a consequence of either Vandiver's conjecture or of Greenberg's conjecture that \(\lambda^+=0\). The author proves that \(\lambda^+=0\) if and only if every CW series f(T), which satisfies \(f(\zeta_ n-1)\) is a unit of \({\mathbb{Q}}(\zeta_ n)\) for all n, belongs to \(\bar R\). Here \(\zeta_ n\) is a primitive \(p^{n+1}\)-st root of unity, R is the set of rational, global CW series and \(\bar R\) denotes its topological closure.
reviewed by: Charles J. Parry
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 11S20
zbMATH DE Number: 3855239
zbMATH Keywords: Coates-Wiles series
zbMATH Keywords: vanishing of Iwasawa lambda plus invariant
zbMATH Keywords: \({\mathbb{Z}}_ p\)-extension
zbMATH Keywords: CW series
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3855239