Further improvements to the Chevalley-Warning theorems

David B. Leep, Rachel L. Petrik

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 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.

Original languageEnglish
Article number102194
JournalFinite Fields and Their Applications
StatePublished - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.


  • Chevalley-Warning theorem
  • Finite fields
  • Homogeneous forms
  • Number of zeros

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • General Engineering
  • Applied Mathematics


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