Equivariant Forms

Abstract

The goal of this thesis is to develop the theory of the so-called equivariant forms. Precisely, we study and classify all meromorphic functions of the extended upper-half plane h* that commute with the action of a finite index subgroup of SL 2( Z ) on h* . It is shown that they are intimately connected to modular forms, differential forms and quasimodular forms, and hence inherit their structures. A close connection with different geometric objets such as differential forms and sections of line bundles is also established. Finally, to show more the richness of such objects, some applications to the critical points of modular forms are given.