Mathematical Sciences: The Weil-Siegel Formula and Its Applications

本课题由自同构形式理论和L函数理论中的几个问题组成。第一个问题涉及Weil-Siegel公式的推广和应用。第二部分是利用翘板对偶理论研究某些自同构型的算术性质。我们还将研究Clifford代数的结构，以及与某些测地圈有关的上同调类。这项研究属于数论的一般领域。它涉及到表示理论在自同构形和数论中的应用的各个方面。过去，主要研究者在有界域上的自同构函数领域得到了一些有穿透力的结果。预计本项目所考虑的领域将出现新的令人振奋的发展。

This project consists of several problems in the theory of automorphic forms and L-functions. The first problem concerns extending the Weil-Siegel formula and applying this extension. The second concerns the application of the theory of seesaw dual pairs to study arithmetic properties of certain automorphic forms. Research will also be done on the structure of Clifford algebras, as well as, the cohomology classes associated to certain geodesic cycles. This research is in the general area of number theory. It is concerned with various aspects of representation theory in its application to automorphic forms and number theory. The principal investigator has in the past evolved some penetrating results in the area of automorphic functions on bounded domains. New and exciting developments in the areas considered in this project are anticipated.