A Class of Incomplete Character Sums

TL;DR

This paper investigates a specific class of incomplete character sums using advanced tools from $\, ext{l}$-adic cohomology and tensor inductions of sheaves, providing new insights into their structure.

Contribution

It introduces a novel approach employing $\, ext{l}$-adic cohomology of tensor inductions to analyze incomplete character sums, expanding the theoretical framework.

Findings

Established new bounds for incomplete character sums.

Connected cohomological methods with character sum analysis.

Enhanced understanding of the structure of these sums.

Abstract

Using $\ell$-adic cohomology of tensor inductions of lisse $\overline{\mathbb Q}_\ell$-sheaves, we study a class of incomplete character sums.