Fourier Coefficients, L-functions, and Endoscopy Correspondences of Automorphic Forms

自守形式的傅里叶系数、L 函数和内窥镜对应

• 批准号: 1301567
• 负责人: Dihua Jiang
• 金额: $ 18.11万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1301567&HistoricalAwards=false
• 关键词: Fourier; Coefficients; functions; Endoscopy; Correspondences

The PI, Dihua Jiang, has been working on some basic problems related to Automorphic L-functions and explicit Langlands functorial transfers for square-integrable automorphic forms. He investigates the basic structures of the discrete spectrum of automorphic forms and the related problems on the Langlands functoriality. In the local theory, his research attacks the local Langlands conjectures and related basic problems in harmonic analysis of p-adic groups. His long term goal is to understand the general local-global-automorphic principles in the theory of automorphic forms, which reflects one of the basic principles in the arithmetic and number theory.The PI, Dihua Jiang, is an expert in the modern theory of automorphic forms and the Langlands Program. Automorphic forms are functions with abundant symmetries. These symmetries are the guidelines to understand the intrinsic structures of objects in our universe. In Mathematics, these symmetries are common grounds for many different theories such as Geometry, Number Theory, Mathematical Physics, Algebra and Analysis. Hence the modern theory of automorphic forms, essentially the Langlands program, provides the organizing principle for further research in these areas. The research of Dihua Jiang establishes basic structures for automorphic forms and hence yields essential contribution to the Langlands program.

PI Dihua Jiang一直致力于与自动型L功能和明确的Langlands功能转移有关的一些基本问题，以进行方形综合自动形式。他研究了自动形式的离散频谱的基本结构以及兰兰兹功能性的相关问题。在本地理论中，他的研究攻击了当地的兰兰兹猜想和与P-ADIC组的谐波分析中的相关基本问题。他的长期目标是了解自称形式理论中的一般局部全球自动形态原则，这反映了算术和数理论中的基本原理之一。自动形式是具有丰富对称性的函数。这些对称性是了解我们宇宙中对象的内在结构的准则。在数学中，这些对称性是许多不同理论的共同基础，例如几何，数量理论，数学物理，代数和分析。因此，现代的汽车形式理论，本质上是兰兰兹计划，为这些领域的进一步研究提供了组织原则。 Dihua Jiang的研究建立了汽车形式的基本结构，因此对Langlands计划产生了重要的贡献。