Zeta values as moments: A random matrix theory

par Hartmut Monien (University Bonn & IHES)

vendredi 16 oct. 2026, 15:00 → 16:30 Europe/Paris

Salle Marie-Louise Dubreil-Jacotin (IHP - Bâtiment Borel)

Values of the Riemann zeta-function $\zeta\left(\alpha+\beta n\right)$ with $\alpha>1$, $\beta>0$ and $n$ a positive integer can be obtained as moments of a certain probability distribution. In my talk I will construct the corresponding random matrix model and determine its asymptotic spectral curve, which exhibits an unusual feature, the complete asymptotics of its partition function and uniform approximations to its correlation functions using a discrete version of Riemann-Hilbert problem with Airy and Bessel asymptotics. This relates a problem in number theory to ideas of Vershik and Okounkov in representation theory of the symmetric group.