Improvements upon the Chevalley-Warning-Ax-Katz-type estimates

DOI10.1016/j.jnt.2006.04.003zbMath1201.11004OpenAlexW2054196558MaRDI QIDQ863962

Qi Sun, Wei Cao

Publication date: 12 February 2007

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.04.003

zbMATH Keywords

finite fieldsolutions of equations\(p\)-adic reduction

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Congruences; primitive roots; residue systems (11A07) Diophantine equations in many variables (11D72)

Related Items (12)

\(p\)-adic valuations associated to fibers and images of polynomial functions ⋮ Divisibility on point counting over finite Witt rings ⋮ Zeros of polynomials over finite Witt rings ⋮ Dilation of Newton polytope and \(p\)-adic estimate ⋮ Exponential sums over finite fields ⋮ Improvement to Moreno-Moreno's theorems ⋮ Divisibility of exponential sums via elementary methods ⋮ 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 ⋮ Polynomials meeting Ax’s bound ⋮ Exact $p$-divisibility of exponential sums via the covering method

Cites Work

• Unnamed Item
• A reduction for counting the number of zeros of general diagonal equation over finite fields
• A note on the proof of a theorem of Katz
• On the p-adic Theory of Exponential Sums
• $p$-adic estimates for exponential sums and the theorem of Chevalley-Warning
• 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

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