On a certain additive divisor problem

TL;DR

This paper establishes an asymptotic formula with a power-saving error term for a variant of the binary additive divisor problem involving linear factors, providing uniform results across all parameters.

Contribution

It introduces a new asymptotic formula for a specific additive divisor problem variant with improved error bounds and parameter uniformity.

Findings

Asymptotic formula with power-saving error term

Uniformity in all involved parameters

Enhanced understanding of additive divisor problems

Abstract

We prove an asymptotic formula for a variant of the binary additive divisor problem with linear factors in the arguments, which has a power saving error term and which is uniform in all involved parameters.