Squarefree Values of Random Polynomials

Source abstract

In this paper we consider the error term in the expected count of squarefree values of a polynomial when evaluated at integers $n\le N$. We prove a power saving on average over polynomials of fixed degree and height at most $H$. Our results improve previous estimates of Browning and Shparlinski in that the required range of $H$ is independent of the degree, but depends on $N$