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

Published online by Cambridge University Press:  30 November 2011

M. MÖLLER  and
A. D. POHL
M. MÖLLER
Affiliation:
Goethe-Universität Frankfurt, Institut für Mathematik, 60325 Frankfurt (Main), Germany (email: [email protected])
A. D. POHL
Affiliation:
ETH Zürich, Departement Mathematik, Rämistrasse 101, 8092 Zürich, Switzerland (email: [email protected])
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Abstract

We characterize Maass cusp forms for any cofinite Hecke triangle group as 1-eigenfunctions of appropriate regularity of a transfer operator family. This transfer operator family is associated to a certain symbolic dynamics for the geodesic flow on the orbifold arising as the orbit space of the action of the Hecke triangle group on the hyperbolic plane. Moreover, we show that the Selberg zeta function is the Fredholm determinant of the transfer operator family associated to an acceleration of this symbolic dynamics.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 1 , February 2013 , pp. 247 - 283
Copyright
Copyright © Cambridge University Press 2011

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