Automorphic representations and applications

自守表示及应用

• 批准号: 0700030
• 负责人: Zhengyu Mao
• 金额: $ 12万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-15 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700030&HistoricalAwards=false
• 关键词: Automorphic; representations; applications

Abstract for the proposal DMS-0700030 of MaoThis work concerns some problems in the theory of automorphic forms. The PI will use the theory of automorphic representations to study problems in half integral weight forms, including algorithm for L-values based on a relation between L-values and Fourier coefficients of half integral weight forms. The PI and others will investigate the generalization of this relation to L-values of automorphic forms on higher ranked groups. The PI will also look at Gindikin-Karpelevich type formulas and investigate their application in relative trace formula.This research is in the 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 in diverse applications in areas such as data transmission and processing, and communication systems.

毛泽东DMS-0700030号提案的摘要本文涉及自守型理论中的一些问题。PI将使用自守表示理论来研究半积分权重形式的问题，包括基于L值和半积分权重形式的傅立叶系数之间关系的L值算法。PI和其他人将研究这种关系的推广到更高排名的群体上的自守形式的L值。PI还将研究Gindikin-Karpelevich型公式，并研究它们在相对迹公式中的应用。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，在不同的应用领域，如数据传输和处理，通信系统。