Abstract
Recently, Dang and Rivière proved a remarkable identity, which expresses the 0-value of the Poincaré series of any surface of negative curvature as a function of the Euler characteristic. Thus, a Dirichlet series defined from the lengths of geodesics has a 0-value that depends solely on the topology of the surface. In this lecture, we prove an analogous theorem for graphs. We take up Dang and Rivière's method, but working on a discrete space requires us to significantly modify certain steps.
