WEBER'S CLASS NUMBER PROBLEM IN THE CYCLOTOMIC ℤ2-EXTENSION OF ℚ, III

DOI10.1142/S1793042111004782zbMath1226.11119OpenAlexW2046953787MaRDI QIDQ3173463

Takashi Fukuda, Keiichi Komatsu

Publication date: 10 October 2011

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042111004782

zbMATH Keywords

class numberGalois theorycyclotomic fieldscomputation

Mathematics Subject Classification ID

Galois theory (11R32) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18)

Related Items (16)

Mahler measure and Weber's class number problem in the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q\) for odd prime number \(p\) ⋮ Generalized Pell's equations and Weber's class number problem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Filtrations of units of Viète field ⋮ Fermat's theorem over some totally real number fields ⋮ Height and Weber's class number problem ⋮ Security analysis of cryptosystems using short generators over ideal lattices ⋮ Class numbers in cyclotomic \(\mathbb{Z}_p\)-extensions ⋮ Tate-Shafarevich groups in the cyclotomic \(\hat{\mathbb{Z}} \)-extension and Weber's class number problem ⋮ A class number calculation of the \(5^{\mathrm{th}}\) layer of the cyclotomic \(\mathbb{Z}_2\)-extension of \(\mathbb{Q}(\sqrt{5})\) ⋮ On the Class Numbers in the Cyclotomic Z29- and Z31-Extensions of the Field of Rationals ⋮ Weber’s Class Number One Problem ⋮ Class numbers of totally real fields and applications to the Weber class number problem ⋮ Triviality of the ℓ-class groups in -extensions of for split primes p ≡ 1 modulo 4 ⋮ On Noether's problem for cyclic groups of prime order

Cites Work

• Weber's class number problem in the cyclotomic \(\mathbb Z_2\)-extension of \(\mathbb Q\). II.
• The ideal class group of the basic \(\mathbb Z_p\)-extension over an imaginary quadratic field
• The ideal class group of the \(\mathbb Z_p\)-extension over the rationals
• Primary components of the ideal class group of an Iwasawa-theoretical Abelian number field
• Certain primary components of the ideal class group of the \(\mathbb Z_p\)-extension over the rationals
• Numerische Bestimmung von Klassenzahlen reeller zyklischer Zahlkörper
• Triviality in ideal class groups of Iwasawa-theoretical abelian number fields
• A numerical study of Weber's real class number calculation
• Ideal Class Groups of Iwasawa-Theoretical Abelian Extensions Over the Rational Field
• Weber's Class Number Problem in the Cyclotomic ℤ₂-Extension of ℚ

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