FWF - PANDP - Power-free values and number of divisors of polynomials

The project "Power-free values and number of divisors of polynomials" focuses on two classical problems from analytic number theory. The first one is the problem of e stimating the number of power-free values of polynomials of two variables, including when the two arguments are prime numbers. This field is important for estimating for example square-free values of polynomials, which have importance in cryptography, without which the security of the modern digital world is unthinkable. The second topic of this project is the problem for the average number of divisors of polynomials, for which there are conjectured magnitudes of growth, but up to now none of these conjectures have been fully verified for polynomials of degree higher than two. At the same time the divisor problem has many implications, including in the recent breakthrough problem for small gaps between primes.