Description | For deep and influential contributions to the semiclassical asymptotics of quantum mechanics and its connection with number theory. He showed that the observed statistics of quantum energy levels imply subtle correlations between classical orbits. hHe penetrated deeply into the asymptotics of untypical systems (quantizations of graphs and torus automorphisms), and mixed chaotic-regular systems (where classical bifurcations dominate the quantum spectrum). Applications and extensions of asymptotics devised for the Riemann zeros led him to powerful resummation methods for quantum eigenvalues. His recent studies of the value distributions (moments) of zeta functions have spectacularly extended previous conjectures. |