Improving an inequality for the divisor function

TL;DR

This paper presents an elementary improvement to an existing explicit bound on the divisor function, leading to a modest enhancement of a sieving inequality for Gaussian sequences.

Contribution

It provides a simpler, more effective bound on the divisor function, improving prior results in sieve theory for Gaussian sequences.

Findings

Improved explicit bound on the divisor function.

Enhanced sieving inequality for Gaussian sequences.

Simplified proof method using elementary techniques.

Abstract

We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.