Improved bound for the $k$-variate Elekes--Rónyai theorem

Yaara Jahn, Orit E. Raz

Let $f\in \mathbb{R}[x_1,\dots ,x_k]$, for $k\ge 2$. For any finite sets $A_1,\dots ,A_k\subset \mathbb{R}$, consider the set $$ f(A_1,\ldots, A_k):=\{f(a_1,\ldots, a_k)\mid (a_1…