  This paper generalizes Bass' work on zeta functions for uniform tree
lattices. Using the theory of von Neumann algebras, machinery is developed to
define the zeta function of a discrete group of automorphisms of a bounded
degree tree. The main theorems relate the zeta function to determinants of
operators defined on edges or vertices of the tree. A zeta function associated
to a non-uniform tree lattice with appropriate Hilbert representation is
defined. Zeta functions are defined for infinite graphs with a cocompact or
finite covolume group action.
