Hecke operators on period functions for the full modular group

Abstract

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 introduced recently by Lewis and Zagier and show how they are related to the Hecke operators on Maass cusp forms. Moreover we give an explicit general compatibility criterion for formal sums of matrices to represent Hecke operators on period functions. An explicit example of such matrices with only nonnegative entries is constructed. 1991 Mathematics Subject Classification: 11F25, 11F67