ncts

In 1970s, Shimura initiated the study of a non-holomorphic operator, the Maass-Shimura operator, which led him to define the notion of almost holomorphic modular forms. He later discovered their role on constructing class fields as well as the connection with periods of CM elliptic curves. In this talk, our first goal is to introduce their positive characteristic counterpart, almost holomorphic Drinfeld modular forms. We further relate them to Drinfeld quasi-modular forms which leads us to generalize the work of Bosser and Pellarin to a certain extend. Moreover, we introduce the Maass-Shimura operator $\delta_k$ in our setting for any nonnegative integer $k$ and investigate the relation between the periods of CM Drinfeld modules and the values at CM points of arithmetic Drinfeld modular forms under the image of $\delta_k$ . If time permits, we also reveal how to construct class fields using such values. This is a joint work with Yen-Tsung Chen.