Weil Sums over Small Subgroups

TL;DR

This paper introduces new bounds on Weil sums over small subgroups in prime finite fields, using algebraic geometry and additive combinatorics, improving upon classical bounds in certain ranges.

Contribution

It provides novel bounds for Weil sums over small subgroups, combining algebraic geometry and additive combinatorics techniques.

Findings

New bounds on Weil sums in small subgroups

Bounds are nontrivial where classical bounds are trivial

Method blends algebraic geometry with additive combinatorics

Abstract

We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from algebraic geometry and additive combinatorics.