The Number of Real Quadratic Fields Having Units of Negative Norm

1993/01/01 by Peter Stevenhagen · 2 citations
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Algebraic Geometry and Number Theory #Quadratic equation #Mathematics #Norm (philosophy) #Heuristic #Quadratic field #Isotropic quadratic form #Binary quadratic form #Set (abstract data type) #Quadratic function #Pure mathematics #Mathematical optimization #Geometry #Computer science

paper · pdf · doi:10.1080/10586458.1993.10504272

openalex publication_date 1993/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study the density of the setof real quadratic fields for which the norm of the fundamental unit equals −1 inside the set of real quadratic fields containing elements of norm −1. A conjectural density is derived from a single heuristic assumption, and experimental data supporting this assumption are given. We finally discuss how close one can get to proving such conjectural densities.

Citations

• On the norms of units in quadratic fields
• Some Density Results for Negative Pell Equations; an Application of Graph Theory
• Orthogonal Matrices Over Finite Fields

Cited by

• On the negative Pell equation
• Fundamental unit (number theory) [wikipedia]