Vol. 262, No. 1, 2013

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A positive density of fundamental discriminants with large regulator

Étienne Fouvry and Florent Jouve

Vol. 262 (2013), No. 1, 81–107
Abstract

We prove that there is a positive density of positive fundamental discriminants D such that the fundamental unit 𝜀(D) of the ring of integers of the field (√D--) is essentially greater than D3.

Keywords
regulator of a real quadratic field, Pell equation
Mathematical Subject Classification 2010
Primary: 11D09
Secondary: 11R11
Milestones
Received: 23 November 2011
Revised: 21 November 2012
Accepted: 22 November 2012
Published: 27 March 2013
Authors
Étienne Fouvry
Laboratoire de Mathématique
Campus d’Orsay, Université de Paris-Sud
Batiment 425 UMR 8628
91405 Orsay Cedex
France
Florent Jouve
Laboratoire de Mathématique
Campus d’Orsay, Université de Paris-Sud
Batiment 425 UMR 8628
91405 Orsay Cedex
France