The \(l\)-class group of the \(\mathbb Z_p\)-extension over the rational field

DOI10.2969/jmsj/06441071zbMath1276.11175OpenAlexW2056958995MaRDI QIDQ1928335

Mitsuko Horie, Kuniaki Horie

Publication date: 3 January 2013

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jmsj/1351516769

zbMATH Keywords

Iwasawa theoryreflection theoremclass number formula\(Z_p\)-extension\(l\)-class group

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23) Other abelian and metabelian extensions (11R20)

Related Items

Non-norm-Euclidean fields in basic \(Z_{l}\)-extensions ⋮ Height and Weber's class number problem ⋮ Tate-Shafarevich groups in the cyclotomic \(\hat{\mathbb{Z}} \)-extension and Weber's class number problem ⋮ On the Class Numbers in the Cyclotomic Z29- and Z31-Extensions of the Field of Rationals

Cites Work

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• A note on class numbers of algebraic number fields
• The ideal class group of the \(\mathbb Z_p\)-extension over the rationals
• The narrow class groups of the \(\mathbb Z_{17}\)- and \(\mathbb Z_{19}\)-extensions over the rational field
• Class numbers and \(\mathbb Z_p\)-extensions
• Numerische Bestimmung von Klassenzahlen reeller zyklischer Zahlkörper
• Zur Struktur der l-Klassengruppe galoisscher Zahlkörper.
• The narrow class groups of some Z_p-extensions over the rationals