On fractional sums of the divisor functions

TL;DR

This paper investigates fractional sums of divisor functions, enhancing previous results in the field by Bordellés and Liu-Wu-Yang through improved analytical techniques.

Contribution

It introduces new methods to refine the bounds and estimates for fractional sums of divisor functions, advancing the theoretical understanding.

Findings

Improved bounds for fractional divisor sums

Enhanced analytical techniques for divisor function sums

Refined estimates compared to previous results

Abstract

In this paper, we consider the fractional sum of the divisor functions. We can improve previous results considered by Bordell\'{e}s \cite{Bo} and Liu-Wu-Yang \cite{LWY}.