A family of four-variable expanders with quadratic growth

Abstract

We prove that if g(x, y) is a polynomial of constant degree d that y 2 − y 1 does not divide g(x 1 , y 1 ) − g(x 2 , y 2 ), then for any finite set A ⊂ R |X| ≫ d |A| 2 , where X := g(