A note on the relative class number of the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q(\sqrt{-p})\).

DOI10.3792/PJAA.88.16zbMath1333.11103OpenAlexW1998134363MaRDI QIDQ413796

Humio Ichimura, Shoichi Nakajima

Publication date: 7 May 2012

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1325264391

zbMATH Keywords

class numberquadratic fieldcyclotomic extensionnon-p part

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18)

Related Items (4)

Biographical Sketch of Professor Humio Ichimura ⋮ A note on the relative class number of the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q(\sqrt{-p})\). II ⋮ Relative class numbers inside the \(p\)th cyclotomic field ⋮ Note on the class number of the \(p\)th cyclotomic field

Cites Work

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• On the 2-part of the ideal class group of the cyclotomic \(\mathbb Z_p\)-extension over the rationals
• The ideal class group of the basic \(\mathbb Z_p\)-extension over an imaginary quadratic field
• The non-p-part of the class number in a cyclotomic \(\mathbb{Z}_p\)-extension
• Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field
• Abschätzungen für die Klassenzahlen der quadratischen Körper

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