# Project Details

### Description

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.

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.

Status | Active |
---|---|

Effective start/end date | 16/09/16 → 15/11/20 |