Mathematical Sciences: Theta Lifting and Cohomology of Discrete Subgroups

在自守形式领域，这项研究利用了 自守形式的构造 与局部域上的群的表示论有关。 虽然局部表征理论的学者已经得到了 关于提升一般酉类的深入结果 表示，自守形式的应用程序往往有 被限制在提升一维字符上。 这 研究涉及全球的一个具体而重要的案例， 解除问题和成功应该提供指导， 今后的一般工作。 这项研究是现代分析和代数的桥梁， 数论和古典数学的表示论 群与经典群上的自守形式。

This research, in the area of automorphic forms, makes use of theta-liftings for the construction of automorphic forms related to the representation theory of groups over local fields. Although scholars in local representation theory have obtained deep results about lifting general classes of unitary representations, the applications to automorphic forms have often been restricted to lifting one-dimensional characters. This research involves a specific and important case of the global lifting problem and success should provide guidance for more general work in the future. This research bridges both Modern Analysis and Algebra and Number Theory and concerns the representation theory of classical groups together with automorphic forms on classical groups.