Period integrals

周期积分

• 批准号: 0245310
• 负责人: Herve Jacquet
• 金额: $ 9.99万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0245310&HistoricalAwards=false
• 关键词: Period; integrals

Abstract for Jacquet DMS-0245310The PI proposes to study certain period integrals defined on spaces of automorphic representations. The two main questions are to determine for which representations the periods are non-zero, and to express if possible the periods (which are globally defined) in terms of local data. The main tool of this investigation is the relative trace formula, the study of which was initiated by the PI. One of the main difficulties is a conjectural combinatorial identity (the fundamental lemma). Recently, the PI has obtained the identity in question is an interesting case. The method may apply to other cases as well.From a broader perspective, Langlands program deals with the harmonic analysis of certain linear operators on the spaces of automorphic functions defined on reductive groups. The eigenvalues are related to L-functions with striking analytic properties. On the other hand, the eigenvalues associated with different groups are related in a simple way. In certain specific cases, the two types of relations can be made more precise and more geometric. The goal of the proposal is to study these specific cases.

对于Jacquet DMS-0245310，PI建议研究定义在自同构表示空间上的某些周期积分。两个主要问题是确定哪些表示的周期是非零的，以及如果可能的话，用本地数据表示(全局定义的)周期。本研究的主要工具是由PI开创的相对迹公式的研究。主要困难之一是猜想的组合恒等式(基本引理)。最近，PI获得了有问题的身份是一起有趣的案件。该方法也适用于其他情况。从更广泛的角度来看，朗兰兹程序处理定义在约化群上的自同构函数空间上的某些线性算子的调和分析。本征值与L函数有关，具有显著的解析性质。另一方面，与不同群相关的本征值以一种简单的方式联系在一起。在某些特定情况下，这两种类型的关系可以变得更精确和更几何。该提案的目标是研究这些具体案例。