Zeros of Diagonal Equations over Finite Fields

DOI10.2307/2047083zbMath0659.10017OpenAlexW4233581962MaRDI QIDQ3808159

Daqing Wan

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2047083

zbMATH Keywords

number of solutionsdiagonal equationAx's theorem

Mathematics Subject Classification ID

Diophantine equations in many variables (11D72) Arithmetic theory of polynomial rings over finite fields (11T55) Diophantine equations (11D99)

Related Items (15)

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 zeros of diagonal cubic forms over finite fields ⋮ Chevalley-Warning at the boundary ⋮ On the number of rational points of certain algebraic varieties over finite fields ⋮ Dilation of Newton polytope and \(p\)-adic estimate ⋮ On diagonal equations over finite fields ⋮ On the number of zeros to the equation \(f(x_1)+\cdots+f(x_n)=a\) over finite fields ⋮ Number of zeros of diagonal polynomials over finite fields ⋮ Divisibility of exponential sums via elementary methods ⋮ The number of solutions of certain equations over a finite field ⋮ A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions ⋮ A partial improvement of the Ax-Katz theorem ⋮ Point count divisibility for algebraic sets over ℤ/𝕡^{ℓ}ℤ and other finite principal rings ⋮ Factorization formulae on counting zeros of diagonal equations over finite fields

Cites Work

• Equations over finite fields. An elementary approach
• Equations et variétés algébriques sur un corps fini
• 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
• On a Theorem of Ax
• Zeroes of Polynomials Over Finite Fields
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Zeros of Diagonal Equations over Finite Fields