Sums of Kloosterman sums over square-free and smooth integers

TL;DR

This paper investigates new properties of sums of Kloosterman sums over square-free and smooth integers, motivated by recent advances in bilinear sums and twisted sums involving Kloosterman sums.

Contribution

It introduces novel questions and results concerning sums of Kloosterman sums over specific integer classes, expanding the understanding of their behavior in number theory.

Findings

New bounds for sums over square-free integers

Results on sums over smooth integers

Insights into twisted Kloosterman sums

Abstract

Recently there has been a large number of works on bilinear sums with Kloosterman sums and on sums of Kloosterman sums twisted by arithmetic functions. Motivated by these, we consider several related new questions about sums of Kloosterman sums parametrised by square-free and smooth integers.