FRG: Collaborative Proposal: Periods of Automorphic Forms and Applications to L-Functions

FRG：协作提案：自同构形式的周期及其在 L 函数中的应用

• 批准号: 1065807
• 负责人: Akshay Venkatesh
• 金额: $ 34.89万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1065807&HistoricalAwards=false
• 关键词: FRG; Collaborative; Proposal; Periods; Automorphic

This project centers around the interactions between periods of automorphic forms, automorphic representations, and arithmetic algebraic geometry. In particular the PIs propose to work on several problems on the general derivative conjecture, analysis and arithmetic of Fourier coefficients on exceptional groups, bounds on heights, computational study of nontempered periods, averages/nonvanishing of derivatives of L-series. Recently the study of periods has yielded new results and proofs about L-functions, breakthroughs towards conjectures about algebraic cycles, and new perspectives on classical questions of representation theory. Combined with other tools, periods have also enhanced our understanding of equidistribution problems and topology on locally symmetric spaces. The PIs are at the forefront of these developments. The proposed framework presents an ambitious plan to work on and formulate conjectures incorporating/connecting the recent groundbreaking works in these areas. The research topic is central to several areas of mathematics (arithmetic geometry, automorphic representation theory, analytic number theory). A long range goal of the project is to establish a network of scientists working in automorphic representations, number theory, and arithmetic geometry. The PIs envision a group of PhD students and post-docs participating actively in the proposed Research Retreats and Annual Workshops. This group would include the 15 PhD students presently advised by the PIs.

该项目围绕自动形式，自态表示和算术代数几何形状之间的相互作用。 特别是，PI提议在特殊组上的傅立叶系数，高度的界限，非倍增时期的计算研究，平均l系列衍生物的平均/非呈现。最近，对时期的研究产生了有关L功能的新结果和证据，对代数周期的猜想的突破以及有关代表理论的经典问题的新观点。结合其他工具，时期还增强了我们对等分分配问题和本地对称空间拓扑的理解。 PI处于这些发展的最前沿。拟议的框架提出了一个雄心勃勃的计划，以制定和制定构成/连接这些地区最近开创性作品的猜想。研究主题对于数学几个领域（算术几何，自动形式理论，分析数理论）至关重要。该项目的一个远距离目标是建立一个从事汽车表示，数理论和算术几何形状的科学家网络。 PIS设想了一群博士生和博士后，积极参加拟议的研究务虚会和年度研讨会。该小组将包括PIS目前建议的15名博士学位学生。