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

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

2005-12-15

arxiv.org/abs/math/0512355v2

J. Reine Angew. Math. 603 (2007), 133--163

Mathematics

Number Theory

30 pages; corrected typos and fixed incomplete proofs in section 3

Scientific paper

10.1515/CRELLE.2007.014

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.

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