Mathematics

The seminar presents the main features of the Riemann Hypothesis and discusses its generalisation to an infinite class of complex functions, the so-called Dirichlet L-functions.  The position of the infinite number of zeros of all the Dirichlet L-functions along the axis with real part equal to 1/2 finds a very natural explanation in terms of one of the most basic phenomena in Statistical Physics, alias the Brownian motion. We present the probabilistic arguments which lead to this conclusion and we also discuss a battery of highly non-trivial tests which support with an extremely high confidence the validity of this result.