On the number of zeros of diagonal cubic forms over finite fields

DOI10.1515/FORUM-2020-0354zbMath1503.11148arXiv2012.11897OpenAlexW3115306033MaRDI QIDQ2126312

Chaoxi Zhu, Shao-Fang Hong

Publication date: 19 April 2022

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.11897

zbMATH Keywords

Gauss sumgenerating functionexponential sumdiagonal cubic formJacobi sumHasse-Davenport relation

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Exponential sums (11T23) Other character sums and Gauss sums (11T24)

Related Items (5)

On the number of zeros of diagonal quartic forms over finite fields ⋮ The number of solutions of diagonal cubic equations over finite fields ⋮ On the number of unit solutions of cubic congruence modulo \(n\) ⋮ On the number of rational points of certain algebraic varieties over finite fields ⋮ On the number of zeros to the equation \(f(x_1)+\cdots+f(x_n)=a\) over finite fields

Cites Work

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• La conjecture de Weil. II
• The number of solutions of certain diagonal equations over finite fields
• Equations et variétés algébriques sur un corps fini
• Some Remarks on the Number of Solutions to the Equationf(X₁) + … +f(X_n) = 0
• $p$-adic estimates for exponential sums and the theorem of Chevalley-Warning
• Zeros of Diagonal Equations over Finite Fields
• Period polynomials and Gauss sums for finite fields
• An Elementary Proof of a Theorem of Katz
• Improvements of the Chevalley-Warning and the Ax-Katz Theorems
• On a Theorem of Ax
• Zeroes of Polynomials Over Finite Fields
• Numbers of solutions of equations in finite fields
• On the number of zeros of diagonal cubic forms
• On the number of zeros of diagonal cubic forms

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