Mathematical Sciences: Zeta Functions and Automorphic Forms

数学科学：Zeta 函数和自同构形式

• 批准号: 9622427
• 负责人: Goro Shimura
• 金额: $ 12.6万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622427&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Zeta; Functions; Automorphic

This award supports an investigation on number-theoretical problems on zeta functions and automorphic forms. The Euler products associated to automorphic forms, Eisenstein series, and the special values of certain zeta functions are the main objects of study. The theory of such Euler products (or zeta functions) is one of the central themes of modern number theory, and Eisenstein series are analytic functions inseparably connected to them. The investigation of special values of zeta functions is relatively new, but has become the subject of increasing interest. This research falls into the general mathematical field of Number Theory. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.

该奖项支持对zeta函数和自守形式的数论问题的调查。与自守形式相关的欧拉积、爱森斯坦级数和某些zeta函数的特殊值是主要的研究对象。这种欧拉乘积（或zeta函数）的理论是现代数论的中心主题之一，爱森斯坦级数是与它们密不可分的解析函数。zeta函数的特殊值的研究是相对较新的，但已成为越来越感兴趣的主题。 本文的研究属于数论中的一般数学领域福尔斯。 数论有其历史根源，在研究整个数字，解决这样的问题，如那些处理整除一 一个数字的另一个。它是数学最古老的分支之一，几个世纪以来出于纯粹的美学原因而受到人们的追求。然而，在过去的半个世纪，它已成为一个不可或缺的工具，在不同的应用领域，如数据传输和处理，通信系统。