Seminar des SFB/TRR 326 GAUSDrinfeld Modular Forms of Arbitrary Rank and Their Partial Derivatives

In the 1980s, David Goss introduced Drinfeld modular forms in the rank two case where the analogy with the setting of elliptic modular forms was quite striking. Recently, using the work of Häberli and Pink, Basson, Breuer, and Pink successfully generalized the theory of Drinfeld modular forms to the arbitrary rank setting and provided explicit examples. In this talk, we describe several identities on the derivatives of Drinfeld modular forms of higher rank and introduce a differential operator acting on the space of such forms. Moreover, we construct a finitely generated algebra containing all the Drinfeld modular forms for the full modular group and discuss its stability under partial derivatives as well as the transcendence of its generators at CM points. This is a joint work with Yen-Tsung Chen.