RIEMANN-HYPOTHESIS AND DYNAMICAL-SYSTEMS

The possible connection of Riemann's Hypothesis on the non trivial zer oes of the zeta function zeta(z) with the theory of dynamical systems, both quantum and classical, is discussed. The conjecture of the exist ence of an underlying integrable structure is analysed, resorting on t he one hand to the link between Riemann's zeta function and the Selber g trace formula, on the other to the relation between the zeroes of ze ta(z) and the Gauss unitary ensemble of random matrices, to which - th rough basic results on the twisted de Rham cohomology - a holonomic sy stem of completely integrable differential equations can be associated .