A positive density of fundamental discriminants with large regulator

Étienne Fouvry, Florent Jouve

Type: Article

Publication Date: 2013-03-27

Citations: 9

DOI: https://doi.org/10.2140/pjm.2013.262.81

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 ‫(ޑ‬ √ D) is essentially greater than D 3 .

Locations

Pacific Journal of Mathematics - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF

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+	A Course in Computational Algebraic Number Theory	1993	Henri Cohen
+	Theorie Des Nombres	2013	Adrien-Marie Legendre
+	Effective lower bounds on large fundamental units of real quadratic fields	1985	Clifford A. Reiter
+	Higher Descent on Pell Conics I. From Legendre to Selmer	2003	Franz Lemmermeyer
+	Real quadratic number fields with large fundamental units	1971	Yoshihiko Yamamoto
+	The class numbers of real quadratic fields of discriminant 4p	1996	E. P. Golubeva
+	Class numbers of indefinite binary quadratic forms II	1985	Peter Sarnak
+ PDF Chat	On the negative Pell equation	2010	Étienne Fouvry Jürgen Klüners
+	Some Density Results for Negative Pell Equations; an Application of Graph Theory	1989	J. E. Cremona R. W. K. Odoni
+	Lengths of the periods of the continued fraction expansion of quadratic irrationalities and on the class numbers of real quadratic fields	1990	E. P. Golubeva