Dynamics of the continued fraction map and the spectral theory of \(\text{SL}(2,\mathbb{Z})\)

DOI10.1007/BF01232667zbMath0811.11037MaRDI QIDQ1319215

Isaac Efrat

Publication date: 26 April 1995

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144146

zbMATH Keywords

dynamical systemspectral theoryperiodic continued fractionsRuelle zeta-functionSelberg's zeta-function\(\text{PSL} (2,\mathbb{Z})\)explicit factorizations

Mathematics Subject Classification ID

Continued fractions and generalizations (11J70) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (13)

Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds ⋮ Continued fraction algorithms, functional operators, and structure constants ⋮ Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume ⋮ Small quotients in Euclidean algorithms ⋮ Reflection positivity. Abstracts from the workshop held November 26 -- December 2, 2017 ⋮ Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant ⋮ A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area ⋮ Asymptotics of class numbers ⋮ Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow ⋮ Series expansions for Maass forms on the full modular group from the Farey transfer operators ⋮ A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions ⋮ Regularity of the Euclid algorithm; application to the analysis of fast GCD algorithms ⋮ Mayer’s transfer operator approach to Selberg’s zeta function

Cites Work

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• On the thermodynamic formalism for the Gauss map
• Some applications of thermodynamic formalism to manifolds with constant negative curvature
• On a family of Hilbert modular Maass forms
• Determinants of Laplacians on surfaces of finite volume
• Selberg zeta functions and Ruelle operators for function fields
• Zeta-functions for expanding maps and Anosov flows
• La théorie de Fredholm
• The thermodynamic formalism approach to Selberg’s zeta function for 𝑃𝑆𝐿(2,𝐙)
• The Selberg trace formula for 𝑃𝑆𝐿₂(𝑅)ⁿ
• On a $\zeta$ function related to the continued fraction transformation
• Class numbers of indefinite binary quadratic forms

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