A correction and further improvements to the Chevalley-Warning theorems

David B. Leep; Rachel L. Petrik

doi:10.1016/j.ffa.2024.102427

A correction and further improvements to the Chevalley-Warning theorems

David B. Leep, Rachel L. Petrik

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Article number	102427
Journal	Finite Fields and Their Applications
Volume	96
DOIs	https://doi.org/10.1016/j.ffa.2024.102427
State	Published - Jun 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

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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10.1016/j.ffa.2024.102427

Cite this

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AB - 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.

KW - Chevalley-Warning theorem

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KW - Homogeneous forms

KW - Number of zeros

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A correction and further improvements to the Chevalley-Warning theorems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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