The ring of quasimodular forms for a cocompact group Original Research Article

We describe the additive structure of the graded ring image of quasimodular forms over any discrete and cocompact group image We show that this ring is never finitely generated. We calculate the exact number of new generators in each weight k. This number is constant for k sufficiently large and equals image where I and image are the ideals of modular forms and quasimodular forms, respectively, of positive weight. We show that image is contained in some finitely generated ring image of meromorphic quasimodular forms with image i.e., the same order of growth as image