Density of power-free values of polynomials II

Abstract

In this paper we prove that polynomials $F(x_1,\cdots ,x_n)\in \mathbb{Z}[x_1,\cdots ,x_n]$ of degree $d\ge 3$, satisfying certain hypotheses, take on the expected density of $(d-1)$-free values. This extends the authors' earlier result where a different method implied the similar statement for polynomials of degree $d\ge 5$.