Kostadinka Lapkova (TU Graz): Density of power-free values of polynomials

 We establish asymptotic formulae for the number of $k$-free values of square-free polynomials $F(x_1,...,x_n)$ with integer coefficients and degree $d\geq 2$ for any $n\geq 1$, including when the variables are prime, as long as $k\geq(3d+1)/4$, generalizing works of Hooley and Browning. We discuss also the case $k=d-1$ for the degrees $d=3,4$, which requires a different approach. This is a joint work with Stanley Yao Xiao.