志村曲線上的自守型式及其相關問題

Abstract

在此研究計畫中，我們將研究志村曲線上的自守形式及其相關問題，包含abelian surfaces with QM、志村曲線上的定義方程式、自守形式、singular moduli、志村曲 線的交集、志村曲線上的Ramanujan-type 等式等等。In this research project, we plan to study automorphic forms on Shimura curves and related problems, such as abelian surfaces with quaternionic multiplication, defining equations of Shimura curves, automorphic forms, singular moduli of Shimura curves, intersection of Shimura curves, Ramanujan-type identities for Shimura curves, and etc.