A dynamical approach to Maass cusp forms

2012/08/30 by Anke Pohl, Anke D. Pohl, Pohl, Anke D.
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #math.DS #math.NT #msc:11F37 #msc:11F67 #msc:37B10 #msc:37C30 #msc:37D35 #msc:37D40

paper · pdf · doi:10.48550/arxiv.1208.6178

32 pages, to appear in Journal of Modern Dynamics

arxiv created 2012/12/20 · arxiv updated 2015/03/20

Abstract

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

Related

• Period functions for Maass cusp forms for Γ₀(p): a transfer operator approach
• An Extension of Hejhal's Algorithm to Infinite Volume Fundamental Domains
• An explicit construction of non-tempered cusp forms on O(1,8n+1)
• A class of non-holomorphic modular forms III: real analytic cusp forms for SL₂(ℤ)
• Cheeger constants of hyperbolic reflection groups and Maass cusp forms of small eigenvalues