Further improvements to the Chevalley-Warning theorems

David B. Leep; Rachel L. Petrik

doi:10.1016/j.ffa.2023.102194

Further improvements to the Chevalley-Warning theorems

David B. Leep
, Rachel L. Petrik

Mathematics

Producción científica: Article › revisión exhaustiva

1 Cita (Scopus)

Resumen

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.

Idioma original	English
Número de artículo	102194
Publicación	Finite Fields and Their Applications
Volumen	89
DOI	https://doi.org/10.1016/j.ffa.2023.102194
Estado	Published - ago 2023

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Publisher Copyright:
© 2023 Elsevier Inc.

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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title = "Further improvements to the Chevalley-Warning theorems",

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.",

keywords = "Chevalley-Warning theorem, Finite fields, Homogeneous forms, Number of zeros",

author = "Leep, \{David B.\} and Petrik, \{Rachel L.\}",

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AU - Petrik, Rachel L.

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AB - 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.

KW - Chevalley-Warning theorem

KW - Finite fields

KW - Homogeneous forms

KW - Number of zeros

UR - https://www.scopus.com/pages/publications/85151253916

UR - https://www.scopus.com/pages/publications/85151253916#tab=citedBy

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DO - 10.1016/j.ffa.2023.102194

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JF - Finite Fields and Their Applications

M1 - 102194

ER -

Further improvements to the Chevalley-Warning theorems

Resumen

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ASJC Scopus subject areas

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