A trace on fractal graphs and the Ihara zeta function

DOI10.1090/S0002-9947-08-04702-8zbMath1216.11081arXivmath/0608060MaRDI QIDQ3629386

Daniele Guido, Michel L. Lapidus, Tommaso Isola

Publication date: 27 May 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608060

zbMATH Keywords

\(C^*\)-algebrafunctional equationsregular graphIhara zeta functiondeterminant formulafractal graphgeometric operatoramenable graphself-similar graphprimitive cycle

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) General theory of (C^*)-algebras (46L05) Other Dirichlet series and zeta functions (11M41) Fractals (28A80)

Related Items

Spectral asymptotics revisited, The number of spanning trees in self-similar graphs, The Ihara zeta function for infinite graphs, Dixmier traces and extrapolation description of noncommutative Lorentz spaces, A \(C^*\)-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and \(L^2\)-Betti numbers, Limiting eigenvalue distribution of random matrices of Ihara zeta function of long-range percolation graphs, Zeta functions of graphs with \(\mathbb Z\) actions, Trace formulas for Schrödinger operators on periodic graphs, Fourier duality for fractal measures with affine scales, Applications of automata and graphs: Labeling-operators in Hilbert space. I

Cites Work

• Bartholdi zeta functions of some graphs
• Zeta functions of finite graphs and coverings. III
• Ihara's zeta function for periodic graphs and its approximation in the amenable case
• A \(C^*\)-algebra of geometric operators on self-similar CW-complexes. Novikov-Shubin and \(L^2\)-Betti numbers
• Rotation numbers for automorphisms of \(C^ *\)-algebras
• An index theorem on open manifolds. I. II
• The spectrum of an infinite graph
• Geometry of growth: approximation theorems for \(L^2\) invariants
• A note on the zeta function of a graph
• Zeta functions of finite graphs and coverings. II
• Tree lattices. With appendices by H. Bass, L. Carbone, A. Lubotzky, G. Rosenberg, and J. Tits.
• Counting paths in graphs
• Green functions on self-similar graphs and bounds for the spectrum of the Laplacian
• 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
• Convergence of zeta functions of graphs
• The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps
• ON ZETA AND L-FUNCTIONS OF FINITE GRAPHS
• A Survey on Spectra of infinite Graphs
• A Combinatorial Proof of Bass’s Evaluations of the Ihara-Selberg Zeta Function for Graphs
• Asymptotics of the transition probabilities of the simple random walk on self-similar graphs
• Growth of Self‐Similar Graphs
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE
• ARTIN TYPE L-FUNCTIONS AND THE DENSITY THEOREM FOR PRIME CYCLES ON FINITE GRAPHS
• A SEMICONTINUOUS TRACE FOR ALMOST LOCAL OPERATORS ON AN OPEN MANIFOLD
• Fractal Geometry, Complex Dimensions and Zeta Functions
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
• Zeta functions of discrete groups acting on trees
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