Hecke operators on period functions for the full modular group

Details Hecke operators on period functions for the full modular group Hecke operators on period functions for the full modular group

2004-07-06

arxiv.org/abs/math/0407081v2

IMRN2004, no. 77, 4127-4148

Mathematics

Number Theory

corrected Version, 18 pages

Scientific paper

Matrix representations of Hecke operators on classical holomorphical cusp forms and corresponding period polynomials are well known. In this article we define Hecke operators on period functions and show that they correspond to the Hecke operators on Maass cusp forms. Moreover we give an explicite general compatibility criterion for formal sums of matrices to represent Hecke operators ob period functions. An explicite example with only nonnegative entries in the matrices is constructed.

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