A correction and further improvements to the Chevalley-Warning theorems

David B. Leep, Rachel L. Petrik

Research output: Contribution to journalArticlepeer-review


This paper corrects an error in the proof of Theorem 1.4 (3) of our earlier paper, Further Improvements to the Chevalley-Warning Theorems. The error originally appeared in Heath-Brown's paper, On Chevalley-Warning Theorems, which invalidates the proof of Theorem 2 (iii) in that paper. In this paper, we use a new method to give a correct proof of Theorem 1.4 (3). The correction in this paper also fixes the proof of Theorem 2 (iii) in Heath-Brown's paper. The proof in this paper provides slightly stronger estimates for some of the inequalities that were used in Further Improvements to the Chevalley-Warning Theorems.

Original languageEnglish
Article number102427
JournalFinite Fields and Their Applications
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© 2024 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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