Ihara Zeta functions of infinite weighted graphs

2014/02/20 by Deitmar, Antonius
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1402.4945

Abstract

The theory of Ihara zeta functions is extended to infinite graphs which are weighted and of finite total weight. In this case one gets meromorphic instead of rational functions and the classical determinant formulas of Bass and Ihara hold true with Fredholm determinants.

Related

• The Ihara expression of a generalization of the weighted zeta function on a finite digraph
• On the Ihara expression for the generalized weighted zeta function
• The Ihara Zeta function for infinite graphs
• A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice
• The Ihara expression for generalized weighted zeta functions of Bartholdi type on finite digraphs