Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T05:34:45.913Z Has data issue: false hasContentIssue false
  • English
  • Français

On Units and Class Numbers of Pure Cubic Fields

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  21 December 2009

Nils Reich
Nils Reich
Affiliation:
Seminar for Applied Mathematics, ETH Zurich, Raemistrasse 101, 8092 Zurich, Switzerland E-mail: [email protected]
Get access

Abstract

This is a study of relations between pure cubic fields and their normal closures. Explicit formula shows how the discriminant, regulator and class number of the normal closure can be expressed in terms of the cubic field.

MSC classification

Secondary: 11R16: Cubic and quartic extensions 11R29: Class numbers, class groups, discriminants
Type
Research Article
Information
Mathematika , Volume 52 , Issue 1-2 , December 2005 , pp. 87 - 91
Copyright
Copyright © University College London 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Borevich, C.M. and Shafarevich, I.R.. Number Theory. Academic Press (New York, 1966).Google Scholar
2Dedekind, R.. Über die Anzahl der Idealklassen in reinen kubischen Zahlkörpern. In Mathematische Werke, Chelsea Publishing Company (New York, 1969), 148–233.Google Scholar
3Hasse, H.. Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage. Mathematische Zeitschrift, 31 (1930), 565–582.Google Scholar
4Ismaili, M.C. and El Mesaoudi, R.. Sur la divisibilité exacte par 3 du nombre du classes de certains corps cubiques pure. Ann. Sci. Math. Quebec, 25 (2001), 153–177.Google Scholar
5Neukirch, J.. Algebraische Zahlentheorie. In Ein Jahrhundert Mathematik 1890–1990, pages 587–628. Vieweg & Sohn (Braunschweig, 1990).CrossRefGoogle Scholar
6Neukirch, J.. Algebraic Number Theory. Springer-Verlag (New York, 1999).Google Scholar
7Tate, J.T.. Global class field theory. In Algebraic Number Theory, Academic Press (New York, 1967), 162–203.Google Scholar