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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

基本信息

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

项目摘要

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，一直致力于与自守L-函数和平方可积自守形式的显式Langlands函子转移相关的一些基本问题。他研究自守形式的离散谱的基本结构和朗兰兹函性的相关问题。在局部理论中，他的研究攻击了p-adic群的调和分析中的局部朗兰兹定理和相关的基本问题。他的长期目标是理解自守形式理论中的一般局部-整体-自守原理，这反映了算术和数论的基本原理之一。PI，Dihua Jiang，是现代自守形式理论和朗兰兹纲领的专家。自守形式是具有丰富对称性的函数。这些对称性是理解我们宇宙中物体的内在结构的指导方针。在数学中，这些对称性是许多不同理论的共同基础，如几何，数论，数学物理，代数和分析。因此，自守形式的现代理论，主要是朗兰兹纲领，为这些领域的进一步研究提供了组织原则。姜迪华的研究为自守形式建立了基本结构，从而对朗兰兹纲领做出了重要贡献。