Journal of Modern Dynamics (JMD)

A dynamical approach to Maass cusp forms

Pages: 563 - 596, Issue 4, October 2012      doi:10.3934/jmd.2012.6.563

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Anke D. Pohl - Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3–5, 37073 Göttingen, Germany (email)

Abstract: For nonuniform cofinite Fuchsian groups $\Gamma$ that satisfy a certain additional geometric condition, we show that the Maass cusp forms for $\Gamma$ are isomorphic to $1$-eigenfunctions of a finite-term transfer operator. The isomorphism is constructive.

Keywords:  Maass cusp forms, transfer operator, period functions, symbolic dynamics, geodesic flow.
Mathematics Subject Classification:  Primary: 11F37, 37C30; Secondary: 37B10, 37D35, 37D40, 11F67.

Received: September 2012;      Available Online: January 2013.