Bounds on bilinear sums of Kloosterman sums

TL;DR

This paper introduces a new bound on bilinear sums involving weighted Kloosterman sums, providing an alternative approach to recent results in the field.

Contribution

It offers a novel elementary method to bound bilinear sums of Kloosterman sums, complementing existing advanced techniques.

Findings

New bound on bilinear sums with weighted Kloosterman sums

Complementary to recent results by Kowalski, Michel, and Sawin

Uses elementary arguments for the derivation

Abstract

We use some elementary arguments to obtain a new bound on bilinear sums with weighted Kloosterman sums which complements those recently obtained by E. Kowalski, P. Michel and W. Sawin (2020).