Correlations of representation functions of binary quadratic forms

TL;DR

This paper investigates the relationships between representation functions of binary quadratic forms, extending previous work to include indefinite forms, and explores their correlations in a broader mathematical context.

Contribution

It introduces a framework for analyzing correlations of representation functions of indefinite binary quadratic forms, expanding upon prior work limited to positive definite forms.

Findings

Extended correlation analysis to indefinite forms

Identified new patterns in representation functions

Broadened understanding of quadratic form representations

Abstract

This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.