2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115151Suppose $Y$ is a regular covering of a graph $X$ with covering transformation group $π= \mathbb{Z}$. This paper gives an explicit formula for the $L^2$ zeta function of $Y$ and computes examples. When $π= \mathbb{Z}$, 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.16 pages, 3 figuresNumber TheoryCombinatorics11M41text