Abstract
Hecke operators on rational period functions on the modular group have beend defined based on modular integrals. We give a purely algebraic definition of Hecke operators of rational period functions on the Hecke groups \( G({\sqrt 2}) \) and \( G({\sqrt 3}) \) and investigate their main properties. This is done with the help of description on the action of Hecke operators on rational period functions on the modular group.
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