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<p>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. In addition, 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.</p>

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Zeta Functions of Geometrically Finite Graphs of Groups

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Soonki Hong,
  • Sanghoon Kwon

摘要

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. In addition, 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.