## The PIMS Postdoctoral Fellow Seminar: Paul Péringuey

- Date: 11/22/2023

Online

Around Artin's primitive root conjecture

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.

**Speaker biography:** Paul Péringuey is a PIMS Postdoctoral fellow at the University of British Columbia where he is working with Prof. Greg Martin, under the sponsorship of the PIMS Collaborative Research Group "L-Functions in Analytic Number Theory". He obtained his PhD in 2022 at Université de Lorraine under the supervision of Cécile Dartyge. His area of research is in Analytic Number Theory, Comparative Prime Number Theory, as well as Additive Combinatorics.

This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series.

This seminar takes places across multiple time zones: 9:30 AM Pacific/ 10:30 AM Mountain / 11:30 AM Central

Register via Zoom to receive the link (and reminders) for this event and the rest of the series.

See past seminar recordings on MathTube.