An application of Jacquet-Langlands correspondence to transfer operators for geodesic flows on Riemann surfaces

TL;DR

This paper leverages the Jacquet-Langlands correspondence to relate transfer operators for geodesic flows on Riemann surfaces by comparing their Selberg zeta functions, offering a novel approach in spectral analysis.

Contribution

It introduces a new application of the Jacquet-Langlands correspondence to connect transfer operators across different cofinite Fuchsian groups.

Findings

Established a relationship between transfer operators via Selberg zeta functions

Demonstrated the applicability of Jacquet-Langlands correspondence in spectral transfer

Provided insights into the spectral properties of geodesic flows

Abstract

In the paper as a new application of the Jacquet-Langlands correspondence we connect the transfer operators for different cofinite Fuchsian groups by comparing the corresponding Selberg zeta functions.