A note on the binary additive divisor problem

TL;DR

This paper compares methods for bounding the error term in the binary additive divisor problem, showing they yield the same results and improving an estimate in Motohashi's proof.

Contribution

It demonstrates the equivalence of two different approaches and refines an estimate within Motohashi's method.

Findings

Both methods produce the same upper bound.

An improved estimate in Motohashi's proof.

Enhanced understanding of the error term bounds.

Abstract

In this note we show that the methods of Motohashi and Meurman yield the same upper bound on the error term in the binary additive divisor problem. With this goal, we improve an estimate in the proof of Motohashi.