The quaternionic weighted zeta function of a graph

On the Zeta Function of Quaternionic Shimura Varieties

Weighted Zeta Functions of Graph Coverings

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted L-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

Remarks on the Zeta Function of a Graph

We make two observations about the zeta function of a graph. First we show how Bass’s proof of Ihara’s formula fits into the framework of torsion of complexes. Second, we show how in the special case of those graphs that are quotients of the Bruhat-Tits tree for SL(2, K) for a local nonarchimedean field K, the zeta function has a natural expression in terms of the L-functions of Coexter systems.

Properties Determined by the Ihara Zeta Function of a Graph

In this paper, we show how to determine several properties of a finite graph G from its Ihara zeta function ZG(u). If G is connected and has minimal degree at least 2, we show how to calculate the number of vertices of G. To do so we use a result of Bass, and in the case that G is nonbipartite, we give an elementary proof of Bass’ result. We further show how to determine whether G is regular, a...

A New Bartholdi Zeta Function of a Graph

We define a new type of the Bartholdi zeta function of a graph G, and give a determinant expression of it. Furthermore, we define a new type of the Bartholdi L-function of G, and present a determinant expression for a new type of the Bartholdi L-function of G. As a corollary, we show that a new type of the Bartholdi zeta function of a regular covering of G is a product of new Batholdi L-functio...