# Around Artin's primitive root conjecture

Date: Wed, Nov 22, 2023

Location: Online

Conference: Emergent Research: The PIMS Postdoctoral Fellow Seminar

Subject: Mathematics

Class: Scientific

### Abstract:

In this talk we will first discuss this soon to be 100 years old conjecture, which states that the set of primes for which an integer \(a\) different from \(-1\) or a perfect square is a primitive root admits an asymptotic density among all primes. In 1967 Hooley proved this conjecture under the Generalized Riemann Hypothesis.

After that, we will look into a generalization of this conjecture, where we don't restrain ourselves to look for primes for which \(a\) is a primitive root but instead elements of an infinite subset of \(\mathbb{N}\) for which \(a\) is a generalized primitive root. In particular, we will take this infinite subset to be either \(\mathbb{N}\) itself or integers with few prime factors.