Density of power-free values of polynomials II.

In this paper we prove that polynomials F (x 1 , ⋯ , x n) ∈ Z [ x 1 , ⋯ , x n ] of degree d ≥ 3 , satisfying certain hypotheses, take on the expected density of (d − 1) -free values. This extends the authors' earlier result in [14] where a different method implied the similar statement for polynomials of degree d ≥ 5. [ABSTRACT FROM AUTHOR]