Zeta functions of geometrically finite graphs of groups

2023/02/17 by Soon-Ki Hong, Sanghoon Kwon, Hong, Soonki +1 · 1 citation
Chemistry · Mathematics · #11R59 #Dynamical Systems (math.DS) #FOS: Mathematics #Graph theory and applications #Group Theory (math.GR) #Molecular spectroscopy and chirality #Primary 05C63 #Secondary 20E08 #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.2302.08850

openalex publication_date 2023/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we explore the properties of zeta functions associated with infinite graphs of groups that arise as quotients of cuspidal tree-lattices, including all non-uniform arithmetic quotients of the tree of rank one Lie groups over local fields. Through various examples, we illustrate pairs of non-isomorphic cuspidal tree-lattices with the same Ihara zeta function. Additionally, we analyze the spectral behavior of a sequence of graphs of groups whose pole-free regions of zeta functions converge towards 0, which also presents an example of arbitrary small exponential error-term in counting geodesic formula.

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