On the representation of integers by binary quadratic forms

2017/04/01 by Stanley Yao Xiao, Xiao, Stanley Yao
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1704.00221

openalex publication_date 2017/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we show that for a given irreducible binary quadratic form f(x,y) with integer coefficients, whenever we have f(x,y) = f(u,v) for integers x,y,u,v, there exists a rational automorphism of f which sends (x,y) to (u,v).

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