Note on the class number of the \(p\)th cyclotomic field

DOI10.7169/facm/2015.52.2.8zbMath1388.11076OpenAlexW1504629584MaRDI QIDQ1744832

Shoichi Fujima, Humio Ichimura

Publication date: 20 April 2018

Published in: Functiones et Approximatio. Commentarii Mathematici (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.facm/1434650883

zbMATH Keywords

cyclotomic fieldrelative class numbercomputation

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18)

Related Items (5)

Biographical Sketch of Professor Humio Ichimura ⋮ Quantitative non-vanishing of Dirichlet \(L\)-values modulo \(p\) ⋮ Note on the Class Number of the pth Cyclotomic Field, II ⋮ Relative class numbers inside the \(p\)th cyclotomic field ⋮ Note on the class number of the \(p\)th cyclotomic field. III.

Cites Work

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• A note on the relative class number of the cyclotomic \(\mathbb Z_p\)-extension of \(\mathbb Q(\sqrt{-p})\).
• On the 2-part of the class numbers of cyclotomic fields of prime power conductors
• On the parity of the class number of the field of q-th roots of unity
• Computing the number of totally positive circular units which are squares
• The non-p-part of the class number in a cyclotomic \(\mathbb{Z}_p\)-extension
• An application of the \(p\)-adic class number formula
• On the Iwasawa lambda invariant of an imaginary abelian field of conductor \(3p^{n+1}\)
• A condition for divisibility of the class number of real \(p\)th cyclotomic field by an odd prime distinct from \(p\)
• On the class number of some real abelian number fields of prime conductors
• A Heuristic Asymptotic Formula Concerning the Distribution of Prime Numbers
• Class Number Parity for the pth Cyclotomic Field

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