An Elementary Proof of a Theorem of Katz
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Publication:4732542
DOI10.2307/2374476zbMath0683.12010OpenAlexW1990055659MaRDI QIDQ4732542
Publication date: 1989
Published in: American Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2374476
Polynomials over finite fields (11T06) Other character sums and Gauss sums (11T24) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Congruences in many variables (11D79)
Related Items (21)
On the number of zeros of diagonal quartic forms over finite fields ⋮ On the number of zeros of diagonal cubic forms over finite fields ⋮ A Partition Result for Algebraic Varieties ⋮ Improvements upon the Chevalley-Warning-Ax-Katz-type estimates ⋮ \(p\)-adic valuations associated to fibers and images of polynomial functions ⋮ On the number of rational points of certain algebraic varieties over finite fields ⋮ Divisibility on point counting over finite Witt rings ⋮ Zeros of polynomials over finite Witt rings ⋮ Dilation of Newton polytope and \(p\)-adic estimate ⋮ 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 ⋮ On the \(p\)-adic meromorphy of the function field height zeta function ⋮ On a theorem of Ax and Katz ⋮ Divisibility of exponential sums via elementary methods ⋮ A note on the proof of a theorem of Katz ⋮ A reduction for counting the number of zeros of general diagonal equation over finite fields ⋮ A partial improvement of the Ax-Katz theorem ⋮ Polynomials meeting Ax’s bound ⋮ Zeros of Diagonal Equations over Finite Fields ⋮ The number of rational points of a family of hypersurfaces over finite fields
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