Further Improvements to the Chevalley-Warning Theorems
Number Theory
2022-07-12 v1
Abstract
We study lower bound estimates for the number of solutions of systems of equations over finite fields. Heath-Brown improved the lower bounds given by the classical \emph{Chevalley-Warning Theorems} by excluding systems of equations whose solutions form an affine space. We improve each of Heath-Brown's results and demonstrate sharpness in several cases.
Keywords
Cite
@article{arxiv.2207.04114,
title = {Further Improvements to the Chevalley-Warning Theorems},
author = {David B. Leep and Rachel L. Petrik},
journal= {arXiv preprint arXiv:2207.04114},
year = {2022}
}