A realization of the Hecke algebra on the space of period functions for Gamma_0(n)

Fraczek, M.; Mayer, D.; Mühlenbruch, T.

A realization of the Hecke algebra on the space of period functions for Gamma_0(n)

Authors

Fraczek, M.

Mayer, D.

Mühlenbruch, T.

Description

The standard realization of the Hecke algebra on classical holomorphic cusp forms and the corresponding period polynomials is well known. In this article we consider a nonstandard realization of the Hecke algebra on Maass cusp forms for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to the Maass cusp forms for these groups. This leads also to a simple interpretation of the ``Hecke like'' operators of these authors in terms of the aforementioned non standard realization of the Hecke algebra on the space of vector valued period functions.
30 pages; corrected typos and fixed incomplete proofs in section 3