Certain primary components of the ideal class group of the \(\mathbb Z_p\)-extension over the rationals

DOI10.2748/tmj/1182180736zbMath1202.11050OpenAlexW2090296102MaRDI QIDQ2472597

Kuniaki Horie

Publication date: 22 February 2008

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

Full work available at URL: https://doi.org/10.2748/tmj/1182180736

zbMATH Keywords

cyclotomic fieldclass number formuladecomposition field\(Z_p\)-extensionIdeal class group

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23) Cyclotomic extensions (11R18) Other abelian and metabelian extensions (11R20)

Related Items (14)

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 ⋮ Generalized Pell's equations and Weber's class number problem ⋮ Weber's class number problem in the cyclotomic \(\mathbb Z_2\)-extension of \(\mathbb Q\). II. ⋮ Height and Weber's class number problem ⋮ Security analysis of cryptosystems using short generators over ideal lattices ⋮ 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 ⋮ A class number problem in the cyclotomic \(\mathbb Z_3\)-extension of \(\mathbb Q\) ⋮ Tate-Shafarevich groups in the cyclotomic \(\hat{\mathbb{Z}} \)-extension and Weber's class number problem ⋮ On the 2-part of the class numbers of cyclotomic fields of prime power conductors ⋮ On the Class Numbers in the Cyclotomic Z29- and Z31-Extensions of the Field of Rationals ⋮ Weber’s Class Number One Problem

Cites Work

• Unnamed Item
• The ideal class group of the basic \(\mathbb Z_p\)-extension over an imaginary quadratic field
• Primary components of the ideal class group of the \(\mathbb Z_p\)-extension over \(\mathbb Q\) for typical inert primes
• Class numbers and \(\mathbb Z_p\)-extensions
• Bounds on the Asymptotic Behavior of an Elastic Scattering Amplitude near the Forward Direction
• Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field
• Class Number Computations of Real Abelian Number Fields

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