权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

On Square Integrable Automorphic Forms and Related Problems

关于平方可积自守形式及相关问题

基本信息

批准号：
0653742
负责人：
Dihua Jiang
金额：
$ 19.79万
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：
2007
资助国家：
美国
起止时间：
2007-06-01 至 2011-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0653742&HistoricalAwards=false
关键词：
Square Integrable Automorphic Forms Related

项目摘要

Abstract for the proposal DMS-0653742 of JiangThe Principal Investigator, Dihua Jiang, plans to continue his research on automorphic forms, L-functions and applications to number theory and arithmetic. In general, the PI aims to investigate basic structures of automorphic forms by using harmonic analysis and groups representations. In particular, the PI attacks basic conjectures of R. Langlands in the modern theory of automorphic forms. The proposed research of the PI leads to better understanding the discrete spectrum of the space of square integrable automorphic forms as conjectured by J. Arthur, the related problems on the central values of automorphic L-functions and the corresponding problems in the local theory. Applications to arithmetic of Shimura varieties and to basic problems on Galois groups have been obtained or are expected to be obtained in near future.Basic objects in the universe may be classified by their intrinsic patterns. The basic types of these intrinsic patterns are called types of symmetry, which may be classified mathematically by group representations. Harmonic analysis provides mathematically methods to investigate the symmetric structures via functions. Automorphic functions are special functions with abundant symmetric structures and have natural connections to geometry and number theory. As mathematical subject, automorphic functions have been a very active research area for centuries and will continue to be so for centuries to come. The Principal Investigator, Dihua Jiang, proposes to investigate basic symmetric structures of automorphic functions and their applications to important problems in number theory and arithmetic.

论文摘要：江迪华博士的DMS-0653742号提案主要研究者江迪华博士计划继续他在自守形式、L-函数以及数论和算术应用方面的研究。一般来说，PI旨在通过使用调和分析和群表示来研究自守形式的基本结构。特别是，PI攻击R的基本结构。现代自守形式理论中的朗兰兹。PI的研究有助于更好地理解J.亚瑟提出的平方可积自守型空间的离散谱、自守L-函数的中心值问题以及局部理论中的相应问题。在Shimura簇的算术和Galois群的基本问题上的应用已经得到或有望在不久的将来得到。宇宙中的基本物体可以根据它们的内在模式来分类。这些固有模式的基本类型被称为对称类型，可以通过群表示进行数学分类。调和分析提供了通过函数研究对称结构的数学方法。自守函数是一类具有丰富对称结构的特殊函数，与几何、数论有着天然的联系。自守函数作为数学学科，几个世纪以来一直是一个非常活跃的研究领域，并将在未来几个世纪继续如此。首席研究员江迪华提出研究自守函数的基本对称结构及其在数论和算术中的应用。