Zeta functions of graphs with $\mathbb{Z}$ actions
| dc.creator | Clair, Bryan | |
| dc.date | 2006-07-26 | |
| dc.date.accessioned | 2026-07-07T07:21:00Z | |
| dc.date.available | 2026-07-07T07:21:00Z | |
| dc.description | Suppose $Y$ 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. | |
| dc.description | 16 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0607689 | |
| dc.identifier | http://arxiv.org/abs/math/0607689 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115151 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11M41 | |
| dc.title | Zeta functions of graphs with $\mathbb{Z}$ actions | |
| dc.type | text |