Improvements of the Chevalley-Warning and the Ax-Katz Theorems
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Publication:4764432
DOI10.2307/2375042zbMath0824.11017OpenAlexW2317284968MaRDI QIDQ4764432
Oscar Moreno, Carlos Julio Moreno
Publication date: 15 November 1995
Published in: American Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2375042
Congruences in many variables (11D79) Arithmetic theory of polynomial rings over finite fields (11T55)
Related Items (42)
On the number of zeros of diagonal quartic forms over finite fields ⋮ On the number of zeros of diagonal cubic forms over finite fields ⋮ The number of rational points of certain quartic diagonal hypersurfaces over finite fields ⋮ Functional degrees and arithmetic applications. I: The set of functional degrees ⋮ On the covering radii of a class of binary primitive cyclic codes ⋮ Improvements upon the Chevalley-Warning-Ax-Katz-type estimates ⋮ On the covering radius of some binary cyclic codes ⋮ A New Proof of Warning's Second Theorem ⋮ \(p\)-adic valuations associated to fibers and images of polynomial functions ⋮ A divisibility approach to the open boundary cases of Cusick-Li-Stǎnicǎ's conjecture ⋮ On the number of rational points of certain algebraic varieties over finite fields ⋮ An improvement to Chevalley's theorem with restricted variables ⋮ Divisibility on point counting over finite Witt rings ⋮ Partial zeta functions, partial exponential sums, and \(p\)-adic estimates ⋮ Zeros of polynomials over finite Witt rings ⋮ Dilation of Newton polytope and \(p\)-adic estimate ⋮ Valuation of exponential sums and the generic first slope for Artin-Schreier curves ⋮ Chevalley-Warning type results on abelian groups ⋮ The covering radii of a class of binary cyclic codes and some BCH codes ⋮ On systems of linear and diagonal equation of degree \(p^i+1\) over finite fields of characteristic \(p\) ⋮ Counting rational points of an algebraic variety over finite fields ⋮ Exponential sums over finite fields ⋮ On the number of zeros to the equation \(f(x_1)+\cdots+f(x_n)=a\) over finite fields ⋮ \(p\)-adic valuation of exponential sums associated to trinomials and some consequences ⋮ Hadamard matrices and the spectrum of quadratic symmetric polynomials over finite fields ⋮ Modular periodicity of exponential sums of symmetric Boolean functions ⋮ Recursions associated to trapezoid, symmetric and rotation symmetric functions over Galois fields ⋮ Improvement to Moreno-Moreno's theorems ⋮ Algorithms for modular counting of roots of multivariate polynomials ⋮ Construction of systems of polynomial equations with exact p-Divisibility via the covering method ⋮ Divisibility of exponential sums via elementary methods ⋮ A SPECIAL DEGREE REDUCTION OF POLYNOMIALS OVER FINITE FIELDS WITH APPLICATIONS ⋮ A reduction for counting the number of zeros of general diagonal equation over finite fields ⋮ An improvement of a theorem of Carlitz ⋮ A \(p\)-adic Serre bound ⋮ 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 ⋮ Polynomials meeting Ax’s bound ⋮ Exact $p$-divisibility of exponential sums via the covering method ⋮ The number of rational points of a family of hypersurfaces over finite fields ⋮ Divisibility properties and new bounds for cyclic codes and exponential sums in one and several variables
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