Combinatorial Nullstellensatz approach to polynomial expansion
Volume 165 / 2014
Acta Arithmetica 165 (2014), 279-282 MSC: Primary 12E05; Secondary 05E40. DOI: 10.4064/aa165-3-6
Applying techniques similar to Combinatorial Nullstellensatz we prove a lower estimate of $|f(A,B)|$ for finite subsets $A$, $B$ of a field, and a polynomial $f(x,y)$ of the form $f(x,y)=g(x)+yh(x)$, where the degree of $g$ is greater than that of $h$.