The Ihara zeta function of the infinite grid

zbMath1303.11105arXiv1306.5454MaRDI QIDQ405206

Bryan Clair

Publication date: 4 September 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.5454

zbMATH Keywords

periodic graphsgraph zeta functionssquare grid graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Other Dirichlet series and zeta functions (11M41)

Related Items (5)

A chaotic lattice field theory in one dimension* ⋮ Vertex-face/zeta correspondence ⋮ Grover/zeta correspondence based on the Konno-Sato theorem ⋮ The Ihara zeta function for infinite graphs ⋮ Walk/zeta correspondence

Cites Work

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• Ihara's zeta function for periodic graphs and its approximation in the amenable case
• The arithmetic-geometric mean of Gauss
• Zeta functions of graphs with \(\mathbb Z\) actions
• Convergence of zeta functions of graphs
• Zeta Functions for Infinite Graphs and Functional Equations
• The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps
• Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori
• Zeta functions of discrete groups acting on trees

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