Modular forms of real weights and generalized Dedekind symbols

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