On \({\mathbb{Z}}_ p\)-extensions of real quadratic fields

DOI10.2969/jmsj/03810095zbMath0588.12004OpenAlexW2076380573MaRDI QIDQ1073092

Takashi Fukuda, Keiichi Komatsu

Publication date: 1986

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

Full work available at URL: https://doi.org/10.2969/jmsj/03810095

zbMATH Keywords

class numberreal quadratic fieldprime idealfundamental unitideal class groupGreenberg conjecturetable\({\mathbb{Z}}_ p\)-extensionsvanishing of Iwasawa invariants

Mathematics Subject Classification ID

Quadratic extensions (11R11) Iwasawa theory (11R23) Cyclotomic extensions (11R18)

Related Items (20)

A remark on the \(\lambda\)-invariant of real quadratic fields ⋮ Greenberg's conjecture and relative unit groups for real quadratic fields ⋮ On the Iwasawa invariants of certain real abelian fields ⋮ A note on Greenberg's conjecture for real abelian number fields ⋮ On the Iwasawa \(\lambda_2\)-invariants of certain families of real quadratic fields ⋮ On multiple \(\mathbb Z_p\)-extensions of imaginary abelian quartic fields ⋮ \(p\)-adic approach of Greenberg's conjecture for totally real fields ⋮ Iwasawa's \(\lambda\)-invariants of certain real quadratic fields ⋮ Computation of ℤ₃-invariants of real quadratic fields ⋮ Iwasawa theory for extensions with restricted \(p\)-ramification ⋮ Computation of the Iwasawa invariants of certain real abelian fields. ⋮ On pro-\(p\)-extensions of number fields with restricted ramification over intermediate \(\mathbb{Z}_p\)-extensions ⋮ A note on Greenberg’s conjecture and the abc conjecture ⋮ On capitulation of \(S\)-ideals in \(\mathbb{Z}_p\) ⋮ On the Iwasawa $\lambda $-invariant of the cyclotomic $\mathbb {Z}_2$-extension of $\mathbb {Q}(\sqrt {p} )$ ⋮ Fermat versus Wilson congruences, arithmetic derivatives and zeta values ⋮ Tate-Shafarevich groups in the cyclotomic \(\hat{\mathbb{Z}} \)-extension and Weber's class number problem ⋮ On \(p\)-adic \(L\)-functions and \(\mathbb{Z}_p\)-extensions of certain real abelian number fields ⋮ On the Iwasawa λ-invariant of the cyclotomic ℤ2-extension of ℚ(pq) and the 2-part of the class number of ℚ(pq,2 + 2) ⋮ On \(p\)-adic zeta functions and \(\mathbb{Z}_p\)-extensions of certain totally real number fields

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