Alternatively have a look at the program.

## Generalized Dedekind symbols for modular forms of real weights

Fukuhara defined generalized Dedekind symbols as functions

on P 1(Q) with values in an abelian group satisfying a short list of

relations.

In a previous paper, I have generalized this definition to the case

of possibly non-commutative groups and

constructed 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

## The Fourier-Jacobi-decomposition of Eisenstein series of Klingen type

The space of Siegel modular forms of degree $n$ and weight k has a

decomposition in a direct sum M_n^k=\oplus_{m=0}^{n}M_{n,m}^k, where the

space M_{n,m}^k corresponds to the space of cusp forms of degree m and

weight k. A Siegel modular form of degree n has Fourier-Jacobi

expansions of degree r<=n. The spaces of Jacobi forms have (by work of

Dulinski) similar decompositions.

## Theory of vector-valued modular forms

Modular forms and their generalizations are one of the most central

concepts in number theory. It took almost 300 years to cultivate the

mathematics lying behind the classical (i.e. scalar) modular forms. All

of the famous modular forms (e.g. Dedekind eta function) involve a

multiplier, this multiplier is a 1-dimensional representation of the

underlying group. This suggests that a natural generalization will be

matrix valued multipliers, and their corresponding modular forms are

called vector valued modular forms. These are much richer mathematically