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Applications of Poincaré series on Jacobi groups

Bringmann, Kathrin

German Title: Anwendungen von Poincaré-Reihen auf Jacobi-Gruppen

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Abstract

In meiner Arbeit betrachte ich Anwendungen von Poincaréreihen zur Verallgemeinerten Jacobigruppe. Im ersten Teil schätze ich Fourierkoeffizienten Siegelscher Spitzenformen ab. Zunächst betrachte ich den Fall Siegelscher Spitzenformen kleiner Gewichte zur vollen Siegelschen Modulgruppe, Index g; anschließend untersuche ich eine Untergruppe dieser Gruppe, Index (0,g) und von N. Im zweiten Teil meiner Arbeit geht es um Liftungs-Abbildungen von einem Vektorraum verallgemeinerter Jacobi-Spitzenformen in einen Teilraum elliptischer Spitzenformen.

Translation of abstract (English)

In our work we regard applications of Poincaré series for generalized Jacobi groups. The first part deals with estimates of Fourier coefficents of Siegel cusp forms. First we consider the case of Siegel modular forms for the full modular group having small weight, index g. Afterwards the case of a certain subgroup with index (0,g) and of N is regarded. In the second part we construct lifting maps from a vector space of generalized Jacobi cusp forms to a subspace of elliptic modular forms.

Item Type: Dissertation
Supervisor: Kohnen, Prof. Dr. Winfried
Date of thesis defense: 23 July 2004
Date Deposited: 05 Oct 2004 06:57
Date: 2004
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Poincaré-Reihe, Spitzenform, Siegel-Modulgruppe, Modulgruppe
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