Density of power-free values of polynomials

Kostadinka Lapkova, Stanley Yao Xiao

We establish asymptotic formulae for the number of $k$-free values of polynmilas $F(x_1,\cdots ,x_n)\in \mathbb{Z}[x_1,\cdots ,x_n]$ of degree $d\ge 2$ for any $n\ge 1$, including w…