Hilbert modular and quasimodular forms

Abstract

Quasimodular forms generalize modular forms and have been studied actively in recent years in connection with various topics in number theory and geometry. One of their interesting properties is that they correspond to finite sequences of modular forms of certain types. We extend such a correspondence to the case of Hilbert quasimodular forms. As an application we construct Poincare series for Hilbert quasimodular forms.