Lineare Unabhängigkeit von Hermiteschen Modulformen

In the theory of modular forms it is desired to be able to validate the linear independance of modular forms by calculation. Normally, this is done by the calculation of the Fourier coefficients of the modular forms. In general, no exact bounds are known for the number of Fourier coefficients that are to be calculated in order to verify the linear independance. However, there are several inequalities for Hermitian modular forms. Poor and Yuen showed a method to get better bounds for Siegel modular forms. They improved known properties of the supports of Hermitian modular forms and showed the applicability of the dyadic trace of a matrix to improve the classic inequalities. This work extends this approach to the theory of Hermitian modular forms. After the introduction of the necessary notations to define Hermitan modular forms, minima of hermitan matrices are introduced. These minima are related to the minima of symmetric matrices. A distinct class of functions is introduced which strenghtens the possibilities to test the linear independance of Hermitan modular forms. The dyadic trace, one of these functions, is defined for positive semidefinite matrices. It is a class function which helps to limit the number of Fourier coefficients that have to be calculated. Some calculations are done for the dyadic trace in the cases n=2 and n=3.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2007

Author dc:creator

• Heck, Thorsten

Contributors dc:contributor

• Krieg, Aloys

• info:eu-repo/classification/ddc/510
• Hilbertsche Modulform
• Mathematik
• hilbert modular form

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124048%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:62482