Number Theory Seminar

    

"The density of power-free values of polynomials"

    

In this talk we show that any polynomial $F(x_1, \cdots, x_n)$ with integer coefficients and degree $d \geq 3$ and which satisfy basic necessary conditions take on the expected density of $k$-free values, provided that $k \geq \min\{d-1, 3d/4\}$. This generalizes results of Hooley and Browning, who showed the same result with $n = 1$. This is joint work with K. Lapkova.