Equidistribution of Hecke Eigenforms and Related Problems

Hecke本征型的均匀分布及相关问题

• 批准号: 0855600
• 负责人: Wenzhi Luo
• 金额: $ 19.5万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0855600&HistoricalAwards=false
• 关键词: Equidistribution; Hecke; Eigenforms; Related; Problems

This proposal is centered on problems concerning quantitative equidistribution properties of elliptic Hecke eigenforms and its generalization to higher dimensional arithmetic quotients of Hermitian symmetric spaces, as well as the analytic aspects of automorphic forms and their L-functions related to nonvanishing and subconvexity of the L-values, with the aim to gain deeper understanding of them from analytic perspective. The problems proposed lie at the heart of recent research and development in analytic number theory. This proposal emphasizes different approaches to study these problems, and points interesting connections with other subjects.Automorphic L-function is fundamental object in mathematics. The equidistribution problems proposed to study have origin from quantum mechanics, and is closely related to the theory of automorphic L-function. They are at the interface of number theory, analysis, and geometry.Our approach employs advanced tools from harmonic analysis and number theory, in combination with the new progress from the theory of automorphic representation.It is the rich interplay and interaction of ideas across different fields that we want to pursue in the current proposal.

本文主要研究椭圆Hecke特征型的定量等分布性质及其在厄米对称空间高维算术商中的推广问题，以及自同构形式及其l -函数的解析方面与l值的非消失性和次凸性有关的问题，以期从解析的角度对其有更深入的认识。所提出的问题是解析数论最近研究和发展的核心。这个建议强调了研究这些问题的不同方法，并指出了与其他学科的有趣联系。自同构l函数是数学中的基本对象。提出研究的等分布问题起源于量子力学，并与自同构l函数理论密切相关。它们是数论、分析和几何的交叉点。我们的方法采用了调和分析和数论的先进工具，并结合了自同构表示理论的新进展。我们希望在当前的提案中追求的是不同领域之间丰富的相互作用和相互作用。