Convergence of zeta functions of graphs

2000/07/14 by Bryan Clair, Clair, Bryan, Shahriar Mokhtari-Sharghi +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.math/0007094

8 pages, 1 figure

arxiv created 2000/07/14 · openalex publication_date 2000/07/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The L²-zeta function of an infinite graph Y (defined previously in a ball around zero) has an analytic extension. For a tower of finite graphs covered by Y, the normalized zeta functions of the finite graphs converge to the L²-zeta function of Y.

Related

• Zeta functions of infinite graph bundles
• The Ihara Zeta function for infinite graphs
• Zeta functions of graphs with ℤ actions
• Spectral zeta functions of graphs and the Riemann zeta function in the critical strip
• A functional relation for L-functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L-functions