# Erwan Hillion

Aix-Marseille

### Probabilistic Nyman-Beurling criteria

Linfoot Number Theory Seminar
5th February 2020, 11:00 am – 12:00 pm
Fry Building, 4th Floor Seminar Room

The Nyman-Beurling criterion is an approximation problem in the space of square integrable functions on (0;infty), which is equivalent to the Riemann hypothesis. This involves dilations of the fractional part function by factors \theta_k \in (0; 1), k >= 1. We develop probabilistic extensions of the Nyman-Beurling criterion by considering these \theta_k as random, yielding new structures and criteria.
The main goal of my talk is to explain the interplay between these probabilistic Nyman-Beurling criteria and the Riemann hypothesis.

Joint work with S.Darses.