Combinatorial Nullstellensatz Approach to Polynomial Expanding

preprint2013arXivOpen access

Abstract

Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of ∣f(A,B)∣|f(A,B)| for finite subsets AA, BB of a field, and polynomial f(x,y)f(x,y) of the form f(x,y)=g(x)+yh(x)f(x,y)=g(x)+yh(x), where degree of gg is greater then degree of hh.

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