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

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On a mean value result for a product of $L$-functions

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Speaker: 
Nicole Raulf
Affiliation: 
Univ. Lille
Date: 
Wed, 2017-11-22 14:00 - 14:50
Location: 
MPIM Lecture Hall

The asymptotic behaviour of moments of $L$-functions is of special interest to number theorists and there are conjectures that predict the shape of the moments for families of $L$-functions of a given symmetry type. However, only some results for the first few moments are known. In this talk we will consider the asymptotic behaviour of the first moment of the product of a Hecke $L$-function and a symmetric square L-function. This is joint work with O. Balkanova, G. Bhowmik, D. Frolenkov.

On the structure of mixed weight Hilbert modular forms

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Speaker: 
Hiroki Aoki
Affiliation: 
Tokyo University of Science
Date: 
Wed, 2017-11-22 15:00 - 15:50
Location: 
MPIM Lecture Hall

In this talk we discuss joint work with Sho Takemori on Hilbert modular forms
over the real quadratic field of discriminant 5, with respect to its full modular group.
The graded ring of all Hilbert modular forms of parallel weight were determined by Gundlach.
By using his result and some elementary technique, we establish a structure theorem on mixed
Hilbert modular forms.

Computing weight 1 forms -- a p-adic approach

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Speaker: 
Roberet Pollack
Affiliation: 
Boston University/MPIM
Date: 
Wed, 2017-11-22 16:30 - 17:20
Location: 
MPIM Lecture Hall

The computation of Hecke-eigenforms of weight at least 2 is readily accomplished through the
theory of modular symbols as these Hecke-eigensystems occur in the cohomology of modular
curves.  However, the same is not true for weight 1 modular forms which makes computing
the dimensions of such spaces difficult let alone the actual system of Hecke-eigenvalues. 
Recently effective methods for computing such spaces have been introduced building on an
algorithm of Kevin Buzzard.  In this talk, we present a different, p-adic approach towards

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