Identities in Automorphic Descent

自守下降中的恒等式

• 批准号: 1700637
• 负责人: Zhengyu Mao
• 金额: $ 15.3万
• 依托单位: Rutgers University Newark
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-15 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1700637&HistoricalAwards=false
• 关键词: Identities; Automorphic; Descent

This award supports the principal investigator's research on the theory of automorphic forms, a special topic in the general area of number theory. Number theory has its historical roots in the study of natural numbers. It is among the oldest branches of mathematics. Within the last half century it has become an indispensable tool, with diverse applications in areas such as data transmission and processing, communication systems, and internet security. In more detail, the project centers on the theory of automorphic forms. The main goal of the project is to develop the automorphic descent method, which provides construction of automorphic forms on classical groups. The PI will establish identities relating the constructed automorphic forms to the data used in the descent construction. The PI will also investigate the application of these identities to a quantitative refinement of the Gan-Gross-Prasad conjecture, which is a conjecture that can be viewed as a far-reaching local to global principle for period integrals.

该奖项支持首席研究员对自守形式理论的研究，这是数论一般领域的一个特殊课题。数论的历史根源在于对自然数的研究。它是最古老的数学分支之一。在过去的半个世纪，它已成为一个不可或缺的工具，在数据传输和处理，通信系统和互联网安全等领域的各种应用。 更详细地说，该项目集中在自守形式的理论。该项目的主要目标是开发自守下降方法，它提供了在经典群上构造自守形式。PI将建立将构造的自守形式与下降构造中使用的数据相关联的身份。PI还将研究这些恒等式在Gan-Gross-Prasad猜想的定量改进中的应用，Gan-Gross-Prasad猜想可以被视为周期积分的一个影响深远的局部到全局原理。

项目成果

Whittaker-Fourier coefficients of cusp forms

尖点形式的 Whittaker-Fourier 系数

• 发表时间: 2019
• 期刊: Advanced lectures in mathematics
• 作者: Mao, Zhengyu