Iwasawa's \(\lambda\)-invariants of certain real quadratic fields
type: Item
instance of: scholarly article
title: Iwasawa's \(\lambda\)-invariants of certain real quadratic fields
zbMATH Open document ID: 0703.11055
author: Takashi Fukuda
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: The author continues to study Greenberg's conjecture [\textit{R. Greenberg}, Am. J. Math. 98, 263-284 (1976; Zbl 0334.12013)] in the case of a real quadratic field k. Let p be an odd prime number which splits in k. Two natural \(n_ 1\) and \(n_ 2\) are defined from a prime ideal of k lying over p and the fundamental unit of k [see the author and \textit{K. Komatsu}, J. Math. Soc. Japan 38, 95-102 (1986; Zbl 0588.12004) and the author, \textit{K. Komatsu} and \textit{H. Wada}, Proc. Japan Acad., Ser. A 62, 318-319 (1986; Zbl 0612.12004)]. In this note connected closely with the cited papers the case \(n_ 1=n_ 2=2\) is treated further. In particular it is shown that Iwasawa's invariants \(\mu_ p(k)\) and \(\lambda_ p(k)\) both vanish under certain conditions concerning \(n_ 1\), \(n_ 2\) and the p-primary part of the ideal class group of k(exp(2\(\pi\) i/p)).
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 4152502
zbMATH Keywords: Greenberg's conjecture
zbMATH Keywords: real quadratic field
zbMATH Keywords: Iwasawa's invariants
MaRDI profile type: Publication
full work available at URL: pjaa.65.260
OpenAlex ID: W2057854438
cites work: On \({\mathbb{Z}}_ p\)-extensions of real quadratic fields
cites work: A remark on the \(\lambda\)-invariant of real quadratic fields
cites work: On the Iwasawa Invariants of Totally Real Number Fields
DOI: 10.3792/PJAA.65.260
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description: scientific article; zbMATH DE number 4152502