Abstract:

In the 1980s, David Goss introduced Drinfeld modular forms in the rank two case and revealed several similarities between them and the classical modular forms as well as giving a recipe for how to construct them for the higher rank setting. Later on their higher rank generalization was studied extensively by Basson, Breuer, Gekeler and Pink. In this talk, we introduce a special function on the Drinfeld period domain in the higher rank setting which also generalizes the false Eisenstein series of Gekeler. We also introduce its functional equation, its relation with quasi-periodic functions of a Drinfeld module and the transcendence of its values at CM points. This is a joint work with Yen-Tsung Chen.