Further Improvements to the Chevalley-Warning Theorems

Published 8 Jul 2022 in math.NT | (2207.04114v1)

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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