Nearly holomorphic Drinfeld modular forms and their special values at CM points

Abstract

In the present paper, we introduce the notion of nearly holomorphic Drinfeld modular forms and study an analogue of Maass-Shimura operators in this context. Furthermore, for a given nearly holomorphic Drinfeld modular form, we show that its special values at CM points are algebraically independent whenever the associated endomorphism algebras are distinct. As an application of our results on nearly holomorphic Drinfeld modular forms, we study Drinfeld quasi-modular forms for arbitrary congruence subgroups and investigate the structure of the vector spaces and the algebras generated by them.