Work

Binary quadratic forms with the same value set

Year: 2025

Type: article

Abstract: Given a binary quadratic form F ∈ Z [ X , Y ] , we define its value set F ( Z 2 ) to be { F ( x , y ) : ( x , y ) ∈ Z 2 } . If F , G ∈ Z [ X , Y ] are two binary quadratic forms, we give necessary and sufficient conditions on F and G for F ( Z 2 ) = G ( Z 2 ) .

Source: Indagationes Mathematicae

DOI: 10.1016/j.indag.2025.01.005

Authors: Étienne Fouvry, Peter Koymans

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay, ETH Zurich, ETH Institute for Theoretical Studies

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,140

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek