# Abstracts for Seminar Aachen-Bonn-Köln-Lille-Siegen on Automorphic Forms

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## Generalized Dedekind symbols for modular forms of real weights

Posted in
Speaker:
Yuri Manin
Affiliation:
MPIM
Date:
Tue, 2016-03-01 14:00 - 14:50

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

Posted in
Speaker:
Thorsten Paul
Affiliation:
Saarbruecken
Date:
Tue, 2016-03-01 15:00 - 15:50

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

Posted in
Speaker:
Jitendra Bajpai
Affiliation:
MPIM
Date:
Tue, 2016-03-01 17:00 - 17:50

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

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