The ideal class group of the basic \(\mathbb Z_p\)-extension over an imaginary quadratic field

DOI10.2748/TMJ/1128703003zbMath1128.11051OpenAlexW1969177374MaRDI QIDQ812890

Kuniaki Horie

Publication date: 26 January 2006

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1128703003

zbMATH Keywords

class numberIwasawa theory

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23)

Related Items (15)

WEBER'S CLASS NUMBER PROBLEM IN THE CYCLOTOMIC ℤ₂-EXTENSION OF ℚ, III ⋮ Mahler measure and Weber's class number problem in the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q\) for odd prime number \(p\) ⋮ On the 2-part of the ideal class group of the cyclotomic \(\mathbb Z_p\)-extension over the rationals ⋮ On the Iwasawa lambda invariant of an imaginary abelian field of conductor \(3p^{n+1}\) ⋮ A note on the relative class number of the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q(\sqrt{-p})\). ⋮ Filtrations of units of Viète field ⋮ Weber's class number problem in the cyclotomic \(\mathbb Z_2\)-extension of \(\mathbb Q\). II. ⋮ 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 ⋮ Certain primary components of the ideal class group of the \(\mathbb Z_p\)-extension over the rationals ⋮ Height and Weber's class number problem ⋮ The ideal class group of the \(\mathbb Z_p\)-extension over the rationals ⋮ On the parity of the class number of an imaginary abelian field of conductor \(2^{a} p^{b}\) ⋮ On the 2-part of the class numbers of cyclotomic fields of prime power conductors ⋮ Weber’s Class Number One Problem

Cites Work

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• A note on class numbers of algebraic number fields
• Class numbers and \(\mathbb Z_p\)-extensions
• The non-p-part of the class number in a cyclotomic \(\mathbb{Z}_p\)-extension
• A numerical study of Weber's real class number calculation
• Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field
• Proof of a conjecture of Morris Newman.
• Use of a Computer Scan to Prove Q (√2 + √2) and Q (√3 + √2) are Euclidean
• On the Absolute Class-Group of Abelian Fields

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