Modular forms of real weights and generalized Dedekind symbols

TL;DR

This paper extends the theory of generalized Dedekind symbols to real weight modular forms by utilizing iterated period functions, building on previous work with cusp forms and iterated period polynomials.

Contribution

It introduces a generalized construction of Dedekind symbols for real weight modular forms using iterated period functions, expanding the scope beyond classical integer weights.

Findings

Generalization of Dedekind symbols to real weights

Utilization of iterated period functions for new constructions

Connections to non-commutative structures in modular forms

Abstract

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.