Abstract:   

   Last time we saw how the Selberg Trace Formula relates the dynamics of a Riemann surface with its spectrum. However, the trace formula remained rather obscure, because it was formulated with test functions. This time, we will explain distributions and discuss the example of the Poisson Summation Formula. Then we will reformulate the Selberg Trace Formula as a distribution and show how to derive Weyl's asymptotic law.