报 告 人: 单逸 (University of Toronto)

时间地点: 数学学院新楼 308，5月19日14:00-15:00

题     目: Rationality of quaternionic Eisenstein series on U(2,n)

摘   要: The Eisenstein series form an important family of automorphic forms, and in many cases of holomorphic modular forms, their Fourier coefficients are known to be rational. Recently, a theory on the Fourier expansion of quaternionic modular forms was developed by Pollack for quaternionic exceptional groups, and by Hilado-McGlade-Yan for rank two unitary groups U(2,n).

In this talk, we focus on the even unitary groups U(2,n) that are quasi-split over all  finite places. We will present an explicit Fourier expansion for the quaternionic Heisenberg Eisenstein series of weight l>n+1 on U(2,n). As a consequence, this Fourier expansion is rational in a certain sense and the Fourier coefficients have bounded denominators. This talk is based on joint work with Henry H. Kim.

报告人简介: Dr. Yi Shan is a postdoc at the University of Toronto, and works on automorphic forms and representation theory.