Zeta functions of graphs with [formula omitted] actions

Abstract

Suppose Y is a regular covering of a finite graph X with covering transformation group π = Z . This paper gives an explicit formula for the L 2 zeta function of Y and computes examples. When π = Z , the L 2 zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta functions of regular graphs, such as the location of singularities and the functional equation.