On an approximate functional equation involving the divisor function

TL;DR

This paper improves the error term in the approximate functional equation for exponential sums involving the divisor function under specific parameter conditions.

Contribution

It introduces refined bounds for the error term in the approximate functional equation related to the divisor function.

Findings

Enhanced error estimates for the functional equation

Conditions identified for improved bounds

Potential applications to divisor sum problems

Abstract

The error term in the approximate functional equation for exponential sums involving the divisor function will be improved under certain conditions for the parameters of the approximate functional equation.