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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F02%3A00006842" target="_blank" >RIV/00216224:14310/02:00006842 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

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

Original language description

There is in the literature a lot of deteminant formulae involving the relative class number of an imaginary abelian number field. Most of these formulae can be obtained in a unique way by means of the Stickelberger ideal. Some papers giving the relativeclass number formula for intermediate fields of the cyclotomic Zp-extension of an imaginary abelian field in the form of a product of determinants have appeared recently. The aim of this note is to show that it is not essential to assume that we deal with a layer in the cyclotomic Zp-extension, the similar construction can be done for any extension of abelian fields.

Czech name

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

Czech description

There is in the literature a lot of deteminant formulae involving the relative class number of an imaginary abelian number field. Most of these formulae can be obtained in a unique way by means of the Stickelberger ideal. Some papers giving the relativeclass number formula for intermediate fields of the cyclotomic Zp-extension of an imaginary abelian field in the form of a product of determinants have appeared recently. The aim of this note is to show that it is not essential to assume that we deal with a layer in the cyclotomic Zp-extension, the similar construction can be done for any extension of abelian fields.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F01%2F0471" target="_blank" >GA201/01/0471: Algebraic, analytic and combinatorial methods of number theory</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2002

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Acta Mathematica et Informatica Universitatis Ostraviensis

ISSN

1211-4774

e-ISSN

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Volume of the periodical

10

Issue of the periodical within the volume

1

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

5

Pages from-to

79

UT code for WoS article

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EID of the result in the Scopus database

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