Transfer operators for $\Gamma_{0}(n)$ and the Hecke operators for the period functions of $\PSL(2,\mathbb{Z})$

Abstract

In this paper we report on a surprising relation between the transfer operators for the congruence subgroups these operators are just the well-known Hecke operators on the space of period functions for the modular group, derived previously using the Eichler–Manin–Shimura correspondence between period polynomials and modular forms for this group, and its extension to Maass wave forms by Lewis and Zagier.