eBook

Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume

Bruggeman, Roelof, Pohl, Anke Dorothea

2023

Overview

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.

• Publisher: American Mathematical Society
• Subject: Automorphic forms / Dynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) msc / Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems msc / Functions of a complex variable -- Riemann surfaces -- Fuchsian groups and automorphic functions msc / Hecke algebras / Number theory / Number theory -- Discontinuous groups and automorphic forms -- Automorphic forms, one variable msc / Number theory -- Discontinuous groups and automorphic forms -- Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols msc / Number theory -- Discontinuous groups and automorphic forms -- Spectral theory; Selberg trace formula msc / Number theory-Data processing / Transfer operators
• ISBN: 9781470465452, 1470465450