On a Twisted Version of Linnik and Selberg's Conjecture on Sums of Kloosterman Sums

TL;DR

This paper extends previous work to twisted sums of Kloosterman sums, providing evidence for a conjecture related to the distribution of these sums and their behavior in number theory.

Contribution

It generalizes the Sarnak-Tsimerman approach to twisted sums, advancing understanding of the twisted Linnik-Selberg Conjecture.

Findings

Provides new bounds for twisted Kloosterman sums

Supports the twisted Linnik-Selberg Conjecture with theoretical evidence

Extends methods from untwisted to twisted sum analysis

Abstract

We generalise the work of Sarnak-Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik-Selberg Conjecture.