Verschiedene Aspekte von Modulformen in mehreren Variablen

• Various aspects of modular forms in several variables

Hauffe-Waschbüsch, Adrian; Krieg, Aloys (Thesis advisor); Heim, Bernhard (Thesis advisor)

Aachen : RWTH Aachen University (2021)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2021

Abstract

In the first part of the thesis a statement of Böcherer and Kohnen (2016) about the growth of Fourier coefficients of cusp forms and non-cusp forms is transferred from Siegel modular forms to Hermitian modular forms and orthogonal modular forms. The second part of the thesis constructs the exceptional isomorphism between the symplectic group with respect to Hamiltonian quaternions and the orthogonal group SO(2,6). A method is given to calculate it explicitly. The third and last part deals with Hermitian Maaß-forms of degree 2. In the first half, possible algebraic dependencies between Hermitian Eisenstein series to arbitrary discriminant are investigated using the Fourier expansion. In the second half, a construction of Hermitian measure forms to odd weight and the nontrivial character is given.