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On value sets of polynomials over a field

Zhi-Wei Sun
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Abstract

Let F be any field. Let p(F) be the characteristic of F if F is not of characteristic zero, and let p(F)=+\infty otherwise. Let A_1,...,A_n be finite nonempty subsets of F, and let $$f(x_1,...,x_n)=a_1x_1^k+...+a_nx_n^k+g(x_1,...,x_n)\in F[x_1,...,x_n]$$ with k in {1,2,3,...}, a_1,...,a_n in F\{0} and deg(g) k$ we propose a further conjecture which extends the Erdos-Heilbronn conjecture in a new direction.

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Zhi-Wei Sun. 2008-04-02. On value sets of polynomials over a field. https://arxiv.org/abs/math/0703180

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