# Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

## TL;DR

This paper introduces new bounds on colinear triples in subgroups of prime finite fields and applies these results to improve bounds on exponential sums involving trinomials.

## Contribution

It provides novel bounds on colinear triples in subgroups and leverages these to enhance estimates on exponential sums with trinomials in finite fields.

## Key findings

- New bounds on colinear triples in subgroups of prime finite fields
- Improved bounds on exponential sums with trinomials
- Enhanced understanding of additive and multiplicative structures in finite fields

## Abstract

We give a new bound on colinear triples in subgroups of prime finite fields and use it to give some new bounds on exponential sums with trinomials.