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 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 language | English |
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Article number | 102194 |
Journal | Finite Fields and Their Applications |
Volume | 89 |
DOIs | |
State | Published - Aug 2023 |
Bibliographical note
Publisher Copyright:© 2023 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