演講者：楊一帆教授
單 位：國立交通大學應用數學系
日 期：2012年12月26日 PM 14:30
地 點：國立高雄大學理學院408室
講 題：Hypergeometric functions as automorphic forms on Shimura curves
摘 要：
Shimura curves are generalizations of modular curves and are moduli spaces of principally polarized abelian surfaces with quaternionic multiplication. As in the case of modular curves, we have the notions of automorphic forms and Hecke operators. However, because of the lack of cusps on Shimura curves, there have been very few explicit methods for Shimura curves. In this talk, we will show that automorphic forms on Shimura curves of genus zero can be expressed in terms of solutions of certain second-order ordinary differential equations and we can explicitly compute how Hecke operators act on these functions. In the case of simplest Shimura curves, this gives us many elegant identities and evaluations for hypergeometric functions. This is a followup to my talk given at NUK ten years ago.
