Number Theory Seminar

Date: March 9, 2023

Time: 2:30PM - 3:30PM

Location: BLOC 302

Speaker: Yen-Tsung Chen, Penn State University

Title: On almost holomorphic Drinfeld modular forms and their special values at CM points

Abstract: It is known that the derivative of a modular form is no longer modular. One possible approach to this issue is modifying the differential operator by sacrificing the holomorphy. This leads to the study of nearly holomorphic modular forms and Maass-Shimura operators. The former object was introduced and investigated by Shimura in the 1970s. It also has a strong connection with the quasi-modular forms introduced by Kaneko and Zagier in 1995. In this talk, we introduce the notion of almost holomorphic Drinfeld modular forms and construct an analogue of the Maass-Shimura operators in this context. The structure of almost holomorphic Drinfeld modular forms as well as its connection with Drinfeld quasi-modular forms have been developed. Furthermore, we establish the algebraic independence result for the special values of almost holomorphic Drinfeld modular forms at CM points. This is joint work with Oguz Gezmis.