# Conditional expanding bounds for two-variable functions over arbitrary fields

## TL;DR

This paper improves bounds on how two-variable functions expand over arbitrary fields by applying Rudnev's point-plane incidence bound, refining previous results in the area.

## Contribution

It introduces an improved bound on conditional expanding bounds for two-variable functions over arbitrary fields using Rudnev's incidence theorem.

## Key findings

- Enhanced bounds on expanding functions over arbitrary fields
- Application of Rudnev's point-plane incidence bound to this problem
- Refinement of previous results by Hegyvári and Hennecart

## Abstract

In this short note, we use Rudnev's point-plane incidence bound to improve some results on conditional expanding bounds for two-variable functions over arbitrary fields due to Hegyv\'ari and Hennecart.