Formulae for the relative class number of an imaginary abelian field in the form of a determinant

DOI10.1017/S0027763000007959zbMath1002.11079MaRDI QIDQ2764674

Radan Kučera

Publication date: 10 January 2003

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

generalized Bernoulli numbersMaillet determinantStickelberger elementsintegral group ringDemyanenko matrix

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (7)

Unnamed Item ⋮ Determinant formulas for class numbers in function fields ⋮ On a generalization of the Demjanenko determinant ⋮ A study of Inkeri's class number formula ⋮ A generalization of Maillet and Demyanenko determinants for the cyclotomic \(\mathbb Z_p\)-extension ⋮ Class numbers of some abelian extensions of rational function fields ⋮ Generalizations of Girstmair's formulas

Cites Work

• Unnamed Item
• On Maillet determinant
• The relative class numbers of certain imaginary abelian number fields and determinants
• Demjanenko matrix, class number, and Hodge group
• An index formula for the relative class number of an abelian number field
• On the Stickelberger ideal and the circular units of an abelian field
• On the Stickelberger ideal and the circular units of a cyclotomic field
• On the cosets of the \(2q\)-power group in the unit group modulo \(p\)
• Demjanenko matrix and 2-divisibility of class numbers
• Demjanenko matrix for imaginary abelian fields of odd conductors
• A Demjanenko matrix for abelian fields of prime power conductor
• On the Stickelberger ideal and circular units of a compositum of quadratic fields
• On a special ideal contained in the Stickelberger ideal
• On Demjanenko's matrix and Maillet's determinant for imaginary abelian number fields
• Generalized Maillet determinant

This page was built for publication: Formulae for the relative class number of an imaginary abelian field in the form of a determinant