A reduction for counting the number of zeros of general diagonal equation over finite fields

DOI10.1016/j.ffa.2005.07.001zbMath1169.11055OpenAlexW1982545726MaRDI QIDQ998655

Qi Sun, Wei Cao

Publication date: 9 February 2009

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2005.07.001

zbMATH Keywords

zerosreductionfinite field\(p\)-adicdiagonal equation

Mathematics Subject Classification ID

Diophantine equations in many variables (11D72) Arithmetic theory of polynomial rings over finite fields (11T55)

Related Items (8)

Improvements upon the Chevalley-Warning-Ax-Katz-type estimates ⋮ On the number of rational points of certain algebraic varieties over finite fields ⋮ Dilation of Newton polytope and \(p\)-adic estimate ⋮ Improvement to Moreno-Moreno's theorems ⋮ A SPECIAL DEGREE REDUCTION OF POLYNOMIALS OVER FINITE FIELDS WITH APPLICATIONS ⋮ A partial improvement of the Ax-Katz theorem ⋮ Point count divisibility for algebraic sets over ℤ/𝕡^{ℓ}ℤ and other finite principal rings ⋮ The number of rational points of a family of hypersurfaces over finite fields

Cites Work

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• Representations by bilinear forms in a finite field
• A note on the proof of a theorem of Katz
• On the number of solutions of diagonal equations over a finite field
• On the Solvability of the Equation ∑ n i = 1 x i /d i ≡0 (mod 1) and its Application
• An Elementary Proof of a Theorem of Katz
• Improvements of the Chevalley-Warning and the Ax-Katz Theorems
• Noetherian Subrings of Power Series Rings
• On a Theorem of Ax
• Zeroes of Polynomials Over Finite Fields
• On the Diophantine Equation ∑ n i = 1 x i /d i ≡0 (mod 1)
• Characters over Certain Types of Rings with Applications to the Theory of Equations in a Finite Field
• Numbers of solutions of equations in finite fields
• Congruence Representations in Algebraic Number Fields
• Pairs of Quadratic Equations in a Finite Field
• On diagonal equations over finite fields

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