Expanding polynomials: A generalization of the Elekes-Rónyai theorem to $d$ variables

Orit E. Raz, Zvi Shem Tov

We prove the following statement. Let $f\in \mathbb{R}[x_1,\dots ,x_d]$, for some $d\ge 3$, and assume that $f$ depends non-trivially in each of $x_1,\dots ,x_d$. Then one of the fo…