Artin-Ihara L-functions for hypergraphs

2023/09/27 by Eyler, Mason, Jun, Jaiung
#05C38(primary) #05C65 (secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.15873

Abstract

We generalize Artin-Ihara L-functions for graphs to hypergraphs by exploring several analogous notions, such as (unramified) Galois coverings and Frobenius elements. To a hypergraph H, one can naturally associate a bipartite graph B_H encoding incidence relations of H. We study Artin-Ihara L-functions of hypergraphs H by using Artin-Ihara L-functions of associated bipartite graphs B_H. As a result, we prove various properties for Artin-Ihara L-functions for hypergraphs. For instance, we prove that the Ihara zeta function of a hypergraph H can be written as a product of Artin-Ihara L-functions.

Related

• The Zeta Function of a Hypergraph
• A decomposition formula for the Bartholdi zeta function of a hypergraph covering
• A functional relation for L-functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L-functions
• The special value u=1 of Artin-Ihara L-functions
• Zeta functions of edge-free quotients of graphs