Ashkan Nikeghbali (Zurich)
The CUE and the Riemann zeta function: the microscopic landscape
We provide some convergence results for the characteristic polynomial of random unitary matrices
on the microscopic scale and as a consequence establish several facts about ratios
of characteristic polynomials and correlations for the log of the characteristic polynomial,
thus answering some open problems on that scale.
These answers exhibit a natural random analytic function.
We shall also give evidence about the connection between this object and the
Riemann zeta function and its logarithmic derivative.