Bounds on exponential sums over small multiplicative subgroups

TL;DR

This paper demonstrates that exponential sums over small multiplicative subgroups of finite fields exhibit significant cancellation, highlighting advanced techniques in finite field analysis.

Contribution

It provides an exposition of Bourgain and Chang's arguments, establishing bounds on exponential sums over small subgroups.

Findings

Significant cancellation in exponential sums over small subgroups

Explicit bounds derived for these sums

Methodological insights into Bourgain and Chang's approach

Abstract

We show that there is significant cancellation in certain exponential sums over small multiplicative subgroups of finite fields, giving an exposition of the arguments by Bourgain and Chang.