Computation of the $p$-part of the ideal class group of certain real abelian fields

DOI10.1090/S0025-5718-07-01926-6zbMath1192.11076OpenAlexW1647508908MaRDI QIDQ3426036

Hiroki Sumida-Takahashi

Publication date: 7 March 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01926-6

zbMATH Keywords

Greenberg's conjectureIwasawa invariantideal class groupAbelian field

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23) (K)-theory of global fields (11R70)

Related Items

A generalized problem associated to the Kummer-Vandiver conjecture, Iwasawa-Cohen-Lenstra heuristics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Class fields of abelian extensions of \(\mathbb Q\)
• On the behavior of \(p\)-adic \(L\)-functions at \(s=0\)
• The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
• Remarques sur les unites cyclotomiques et les unites elliptiques
• On the cyclotomic unit group and the ideal class group of a real abelian number field
• Local units modulo Gauss sums
• Computation of the Iwasawa invariants of certain real abelian fields.
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• ON THE IWASAWA INVARIANTS OF CERTAIN REAL ABELIAN FIELDS II
• On the Iwasawa Invariants of Totally Real Number Fields
• Lectures on P-Adic L-Functions. (AM-74)
• The Iwasawa Invariants and the HigherK-Groups Associated to Real Quadratic Fields
• Algorithmic Number Theory
• Irregular primes and cyclotomic invariants to 12 million