Vol. 4, No. 5, 2010

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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
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 (d) and (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