Ichimura-Sumida criterion for Iwasawa \(\lambda\)-invariants
type: Item
instance of: scholarly article
title: Ichimura-Sumida criterion for Iwasawa \(\lambda\)-invariants
zbMATH Open document ID: 0971.11054
author: Takashi Fukuda
author: Keiichi Komatsu
published in: Proceedings of the Japan Academy. Series A
publication date: 2001-02-07T00:00:00Z
review text: Let \(p\) be an odd prime number and \(k\) a cyclic extension of \({\mathbb Q}\) of degree \(p\). The main theorem gives a criterion for the vanishing of the Iwasawa invariant \(\lambda\) for the cyclotomic \({\mathbb Z}_p\) extension of \(k\) in terms of cyclotomic units in the case where \(p\) splits completely in \(k/{\mathbb Q}\). The authors conclude the note by numerical examples. In particular, they show the vanishing of \(\lambda\) for \textbf{all} cyclic cubic fields of prime conductor less than 10.000.
reviewed by: Roland Gillard
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11Y40
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1561769
zbMATH Keywords: vanishing of Iwasawa invariants
zbMATH Keywords: cyclotomic \({\mathbb Z}_p\) extension
zbMATH Keywords: cyclic cubic fields
MaRDI profile type: Publication
full work available at URL: pjaa.76.111
OpenAlex ID: W2049189164
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DOI: 10.3792/PJAA.76.111
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description: scientific article; zbMATH DE number 1561769