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

Project: Research project

Project Details


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.
Effective start/end date16/09/1615/11/20