Zeta functions of discrete groups acting on trees

DOI10.1006/jabr.2000.8600zbMath1013.11057arXivmath/9908068OpenAlexW2029658887MaRDI QIDQ5936188

Bryan Clair, Shahriar Mokhtari-Sharghi

Publication date: 2 July 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9908068

zbMATH Keywords

Ihara-Selberg zeta function for infinite graphs

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Other Dirichlet series and zeta functions (11M41) Groups acting on trees (20E08)

Related Items (18)

Tree-lattice zeta functions and class numbers ⋮ Bartholdi zeta and \(L\)-functions of weighted digraphs, their coverings and products ⋮ Ihara Zeta Functions of Infinite Weighted Graphs ⋮ Graphs, local zeta functions, log-Coulomb gases, and phase transitions at finite temperature ⋮ A new Bartholdi zeta function of a digraph ⋮ The Ihara zeta function of the infinite grid ⋮ Zeta functions of periodic graphs derived from quantum walk ⋮ Convergence of zeta functions for amenable group extensions of shifts ⋮ The Ihara zeta function for infinite graphs ⋮ Heat kernels on regular graphs and generalized Ihara zeta function formulas ⋮ Ihara's zeta function for periodic graphs and its approximation in the amenable case ⋮ Convergence of zeta functions of graphs ⋮ Zeta functions of infinite graph bundles ⋮ Zeta functions of graphs with \(\mathbb Z\) actions ⋮ Bartholdi zeta functions of periodic graphs ⋮ A trace on fractal graphs and the Ihara zeta function ⋮ Zeta functions with respect to general coined quantum walk of periodic graphs ⋮ A generalized Ihara zeta function formula for simple graphs with bounded degree

Cites Work

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• \(L_ 2\)-cohomology and group cohomology
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• Zeta functions of finite graphs and coverings
• On discrete subgroups of the two by two projective linear group over \(p\)-adic fields
• Determinant theory in finite factors
• Uniform Tree Lattices
• ON ZETA AND L-FUNCTIONS OF FINITE GRAPHS
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE

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