International Seminar on Automorphic Forms

Oguz Gezmis (Heidelberg University)

In his series of papers from 1970s, Shimura analyzed a non-holomorphic operator, nowadays called the Maass-Shimura operator, and later extensively studied almost holomorphic modular forms. He also 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 by using such values. This is a joint work with Yen-Tsung Chen.

You can join the Zoom meeting at https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits).