THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW (Q4418317)

scientific article; zbMATH DE number 1961935

Language	Label	Description	Also known as
English	THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW	scientific article; zbMATH DE number 1961935

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instance of

scholarly article

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title

THE PRIME GEODESIC THEOREM AND QUANTUM MECHANICS ON FINITE VOLUME GRAPHS: A REVIEW (English)

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author

Norman E. Hurt

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published in

Reviews in Mathematical Physics

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publication date

7 August 2003

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zbMATH Keywords

Hecke operators

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Selberg-Ihara zeta function

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Axiom A flows

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Selberg eigenvalue conjecture

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Selberg trace formula for finite graphs

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quantum mechanics on finite graphs

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MaRDI profile type

MaRDI publication profile

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cites work

Twisted Perron-Frobenius theorem and $L$-functions

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Homology of closed geodesics in a negatively curved manifold

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Lalley's theorem on periodic orbits of hyperbolic flows

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Periodic orbits and dynamical spectra (Survey)

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A spectral correspondence for Maaß waveforms

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Periodic Orbits for Hyperbolic Flows

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The Equidistribution of Closed Geodesics

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Symbolic Dynamics for Hyperbolic Flows

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Quantum Hall effect on the hyperbolic plane

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<i>L</i> functions in scattering on <i>p</i>-adic multiloop surfaces

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Scattering on univalent graphs from the $L$-function point of view

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Multiloop calculations in p-adic string theory and Bruhat-Tits trees

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Ping-pong groups and closed geodesics in constant negative curvature

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Some negatively curved manifolds with cusps, mixing and counting

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On decay of correlations in Anosov flows

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Prevalence of rapid mixing in hyperbolic flows

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Addendum to ‘Periodic orbits and dynamical spectra’

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Proof of Peterson's conjecture for GL(2) over a global field of $characteristic\quad p$.

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Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces

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Asymptotics for closed geodesics in a homology class, the finite volume case

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Weakly coupled states on branching graphs

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A hierarchic array of integrable models

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A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$

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Some remarks on discrete subgroups of $SL_ 2({\mathbb{C}})$

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ON ZETA AND L-FUNCTIONS OF FINITE GRAPHS

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ARTIN TYPE L-FUNCTIONS AND THE DENSITY THEOREM FOR PRIME CYCLES ON FINITE GRAPHS

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The Selberg trace formula and the Riemann zeta-function

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Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman

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Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II

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On discrete subgroups of the two by two projective linear group over $p$-adic fields

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Homology and Closed Geodesics in a Compact Riemann Surface

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Dynamical 𝐿-functions and homology of closed orbits

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Closed orbits in homology classes

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Periodic orbit theory and spectral statistics for quantum graphs

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PETERSSON'S CONJECTURE FOR CUSP FORMS OF WEIGHT ZERO AND LINNIK'S CONJECTURE. SUMS OF KLOOSTERMAN SUMS

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Distribution of periodic orbits of symbolic and axiom A flows

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Closed geodesics in homology classes on surfaces of variable negative curvature

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Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits

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Eisenstein series and decomposition theory over function fields

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Character sums and abelian Ramanujan graphs (with an appendix by Keqin Feng and Wen-Ch'ing Winnie Li)

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Lattices in rank one Lie groups over local fields

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On Selberg's eigenvalue conjecture

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Quantum ergodicity of eigenfunctions on $\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2$

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Applications of ergodic theory to the investigation of manifolds of negative curvature

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Ramanujan Diagrams

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Natural bounded concentrators

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Bowen's equidistribution theory and the Dirichlet density theorem

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An analogue of the prime number theorem for closed orbits of Axiom A flows

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The Chebotarov theorem for Galois coverings of Axiom A flows

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Geodesics in homology classes

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On the rate of mixing of Axiom A flows

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Meromorphic extensions of generalised zeta functions

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Homology and Closed Geodesics in a Compact Negatively Curved Surface

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Exponential error terms for growth functions on negatively curved surfaces

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Scattering on the Bruhat-Tits tree. I

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Scattering on $p$-adic graphs

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Zeta-functions for expanding maps and Anosov flows

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Class numbers of indefinite binary quadratic forms

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The arithmetic and geometry of some hyperbolic three manifolds

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Bounds for multiplicities of automorphic representations

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Wave chaos in singular quantum billiard

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Closed orbits in homology classes for Anosov flows

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Survey of Spectra of Laplacians on Finite Symmetric Spaces

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On Some Exponential Sums

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Geodesics in homology classes and periods of automorphic forms

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full work available at URL

https://doi.org/10.1142/s0129055x01001009

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Identifiers

zbMATH Open document ID

1081.11506

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DOI

10.1142/S0129055X01001009

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4418317