Ergodic Theory and Dynamical Systems • Vol 40 • No 3
A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions
August 2018 • Alexander Adam, Anke Pohl
Over the last few years Pohl (partly jointly with coauthors) has developed dual ‘slow/fast’ transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for a certain class of hyperbolic surfaces $\unicode[STIX]{x1D6E4}\backslash \mathbb{H}$ with cusps and all finite-dimensional unitary representations $\unicode[STIX]{x1D712}$ of $\unicode[STIX]{x1D6E4}$ . The eigenfunctions with eigenvalue 1 of the fast transfer operators determine the zeros of the Selberg zeta function for $(\uni…