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In a previous paper, I have defined non--commutative generalized Dedekindsymbols for classical $PSL(2,Z)$--cusp forms using iterated period polynomials.Here I generalize this construction to forms of real weights using theiriterated period functions introduced and studied in a recent article byR.~Bruggeman and Y.~Choie.

Modular forms of real weights and generalized Dedekind symbols