Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant

DOI10.1017/S0143385711000794zbMath1277.37048arXiv1103.5235OpenAlexW2962853814MaRDI QIDQ4911072

Anke D. Pohl, Martin Möller

Publication date: 13 March 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.5235

zbMATH Keywords

Hecke triangle groupsFredholm determinantSelberg zeta function

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (14)

Ruelle-Pollicott resonances for manifolds with hyperbolic cusps ⋮ Hecke triangle groups, transfer operators and Hausdorff dimension ⋮ Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds ⋮ Period Functions for Maass Wave Forms and Cohomology ⋮ Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume ⋮ Reflection positivity. Abstracts from the workshop held November 26 -- December 2, 2017 ⋮ Holomorphic Automorphic Forms and Cohomology ⋮ A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area ⋮ Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow ⋮ Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy ⋮ Series expansions for Maass forms on the full modular group from the Farey transfer operators ⋮ Adinkras, dessins, origami, and supersymmetry spectral triples ⋮ A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions ⋮ Dynamics of geodesics, and Maass cusp forms

Cites Work

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• Dynamics of the continued fraction map and the spectral theory of \(\text{SL}(2,\mathbb{Z})\)
• Spaces of holomorphic functions equivalent to the even Maass cusp forms
• Symbolic dynamics for triangle groups
• Eigenfunctions of transfer operators and cohomology
• The Modular Surface and Continued Fractions
• The thermodynamic formalism approach to Selberg’s zeta function for 𝑃𝑆𝐿(2,𝐙)
• Maass cusp forms
• Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval
• Markov systems and transfer operators associated with cofinite Fuchsian groups
• The weyl theorem and the deformation of discrete groups
• Transfer operators for $\Gamma_{0}(n)$ and the Hecke operators for the period functions of $\PSL(2,\mathbb{Z})$
• A Lewis Correspondence for submodular groups
• Period functions for Maass wave forms. I.

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