Scattering on the Poincaré upper half-plane, Riemann hypothesis, intertwining operators and Huygens principle

The famous paper of Faddeev and Pavlov published 45 years ago established a link between scattering theory for the wave equation on non-compact Riemann surfaces and the Riemann hypothesis. I shall describe this approach as well as the links between the Harmonic analysis on semisimple Lie groups and symmetric spaces and scattering theory.