Mathematical Sciences: The Weil-Siegel Formula and Its Applications

数学科学：Weil-Siegel 公式及其应用

• 批准号: 8704375
• 负责人: Stephen Kudla
• 金额: $ 9.69万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8704375&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Weil; Siegel; Formula

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.

本课题主要包括以下几个理论问题： 自守形式和L-函数 第一个问题是 扩展Weil-Siegel公式并应用此扩展。 第二部分是关于跷跷板对偶理论的应用 对研究某些自守的算术性质 forms. 还将对克利福德的结构进行研究 代数，以及与之相关的上同调类 某些测地圈 这项研究是在数论的一般领域。 它 他关注表征理论的各个方面， 应用于自守形式和数论。 的 首席调查员在过去已经发展了一些深入的 结果在有界域上的自守函数的区域。 本报告所述领域的新的和令人兴奋的发展 项目是预期的。