# Multilinear Exponential Sums With A General Class Of Weights

## TL;DR

This paper introduces new bounds for multilinear exponential sums over prime fields with a broader class of weights, leveraging recent advances in incidence geometry and applying results to sparse polynomials and Weyl sums.

## Contribution

It provides novel estimates for multilinear exponential sums with general weights, extending previous work and utilizing recent geometric incidence bounds.

## Key findings

- New bounds for multilinear exponential sums with general weights
- Applications to exponential sums with sparse polynomials
- Improved estimates for Weyl sums over small generalized arithmetic progressions

## Abstract

In this paper we obtain some new estimates for multilinear exponential sums in prime fields with a more general class of weights than previously considered. Our techniques are based on some recent progress of Shkredov on multilinear sums which has roots in Rudnev's point plane incidence bound. We apply our estimates to obtain new results concerning exponential sums with sparse polynomials and Weyl sums over small generalized arithmetic progressions.