### 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.

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