Nalini Anantharaman

On a result by Dang and Rivière

I will present an analogue for discrete graphs of results by Dyatlov-Zworski and Dang-Rivière on surfaces of negative curvature.
These results concern the values at 0 dynamical zeta functions and Poincaré series, and relate these values ​​to the fundamental topological invariant, i.e. the Euler characteristic. In an attempt to better understand their work, I did similar calculations on discrete graphs. All the difficulties of functional analysis disappear (we are in finite dimension) but we lose completely the use of differential geometry.