Value Sets of Polynomials Over Finite Fields

DOI10.2307/2160504zbMath0784.11056OpenAlexW4240415286MaRDI QIDQ4275628

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Publication date: 4 April 1994

Full work available at URL: https://doi.org/10.2307/2160504

zbMATH Keywords

finite fieldupper and lower boundsvalue set of polynomials

Mathematics Subject Classification ID

Polynomials over finite fields (11T06)

Related Items

A refinement of multivariate value set bounds ⋮ Polytope bounds on multivariate value sets ⋮ On the number of distinct values of a class of functions with finite domain ⋮ On value sets of polynomials over a field ⋮ Intersection distribution, non-hitting index and Kakeya sets in affine planes ⋮ On a conjecture of polynomials with prescribed range ⋮ Criteria for equidistribution of solutions of word equations on \(\mathrm{SL}(2)\). ⋮ Value sets of polynomials and the Cauchy-Davenport theorem. ⋮ A probabilistic approach to value sets of polynomials over finite fields ⋮ The number of permutation polynomials of the form f(x) cx over a finite field ⋮ Powers of polynomials and bounds of value sets ⋮ Value Sets of Sparse Polynomials ⋮ A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions ⋮ Additive properties for sets of polynomial values ⋮ Minimal value set polynomials over fields of size 𝑝³

Cites Work

• Value sets of Dickson polynomials over finite fields
• Polynomials with small value set over finite fields
• Permutation polynomials of the form \(x^r f(x^{(q-1)/d)}\) and their group structure
• Linearized polynomials and permutation polynomials of finite fields
• Polynomials with minimal value sets
• A note on polynomials with minimal value set over finite fields
• Polynomials over finite fields with minimal value sets
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