Vol. 4, No. 5, 2010
Download this article
Download this article. For screen
For printing
Recent Issues

Volume 5
Issue 7, 849–1000
Issue 6, 693–848
Issue 5, 567–690
Issue 4, 431–566
Issue 3, 289–429
Issue 2, 131–288
Issue 1, 1–129

Volume 4, Issues 1–8

Volume 3, Issues 1–8

Volume 2, Issues 1–8

Volume 1, Issues 1–4

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)

On the Spiegelungssatz for the 4-rank

Étienne Fouvry and Jürgen Klüners
Vol. 4 (2010), No. 5, 493–508
DOI: 10.2140/ant.2010.4.493
Abstract

Let d be a nonsquare positive integer. We give the value of the natural probability that the narrow ideal class groups of the quadratic fields Q(√d) and Q(√−-d) have the same 4-ranks.
Keywords

quadratic fields, class groups, reflection principle
Mathematical Subject Classification 2000

Primary: 11R29

Secondary: 11R11
Milestones

Received: 2 October 2008
Revised: 30 November 2009
Accepted: 19 January 2010
Published: 10 July 2010
Authors
Étienne Fouvry
Université de Paris-Sud
Laboratoire de Mathématiques
91405 Orsay Cedex
France		 CNRS
91405 Orsay Cedex
France
Jürgen Klüners
Universität Paderborn
Institut für Mathematik
Warburger Straße 100
33098 Paderborn
Germany