Hilbert Modular Forms

Specialeforsvar ved Matthias Likawetz

Titel: Hilbert Modular Forms

Abstract: This thesis studies Hilbert modular forms associated with totally real quadratic fields and its most important properties. To begin with, the Hilbert modular group will be introduced and its action on products of the complex upper half-plane, providing the analytic framework for Hilbert modular forms. We present the important theorem that states the finite dimensionality of Hilbert modular forms. This allows to introduce the Hilbert Eisenstein series which are a crucial example of Hilbert modular forms. Their convergence and modularity properties are established and it is shown how they give rise to non-cuspidal Hilbert modular forms and thus act as a counterpart to cusp forms to complete the space of Hilbert modular forms. Lastly, L-functions of Hilbert modular forms are constructed which are the starting point to dive deeper into the theory of Hilbert modular forms and automorphic representations.

Vejleder: Morten S. Risager

Censor: Jimi Lee Truelsen