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A realization of the Hecke algebra on the space of period functions for Γ0 (n)
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M Fraczek
,
D Mayer
Published/Copyright:
March 12, 2007
Abstract
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 Γ0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Γ0(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 nonstandard realization of the Hecke algebra on the space of vector valued period functions.
Received: 2005-12-14
Published Online: 2007-03-12
Published in Print: 2007-03-27
© Walter de Gruyter
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Articles in the same Issue
- Massey products and ideal class groups
- Purity of exponential sums on 𝔸n, II
- Sheaves on Artin stacks
- Levi umbilical surfaces in complex space
- A realization of the Hecke algebra on the space of period functions for Γ0 (n)
- The 5-canonical system on 3-folds of general type
- On Spin L-functions for GSO10
- Nonexistence of higher codimensional Levi-flat CR manifolds in symmetric spaces
