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arXiv · 2207.04114

Further Improvements to the Chevalley-Warning Theorems

David B. Leep·Rachel L. Petrik
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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.

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David B. Leep, Rachel L. Petrik. 2022-07-08. Further Improvements to the Chevalley-Warning Theorems. https://arxiv.org/abs/2207.04114

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