## A discrete Lefschetz Formula

#### Anton DeitmarExeter University

A Lefschetz formula moulded after the Lefschetz Formula for dynamical systems is given that relates loops in a regular finite graph to traces
of a certain representation. As an application the poles of the Ihara/Bass zeta function are
described in two new ways , the second description uses dimensions of global section spaces of locally constant sheaves, i.e., a version of the Patterson Conjecture is proved.

Back to Automorphic Forms, Group Theory and Graph Expansion