Abstract:
The study of the zeros of the Riemann zeta function constitutes one of the most challenging problems in mathematics. A large literature in devoted to the study of the behavior of the zeta zeros. We will discuss how tools from stochastic analysis, and in particular from Malliavin calculus (multiple integrals, Wiener chaos, Stein method etc) can be used in the study of some aspects of the behavior of the zeta function.