Studies in Automorphic Representations

自守表示研究

• 批准号: 9401466
• 负责人: Jonathan Rogawski
• 金额: $ 12.72万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401466&HistoricalAwards=false
• 关键词: Studies; Automorphic; Representations

9401466 Rogawski This award funds the investigations of Professor Jonathan Rogawski in the theory of automorphic representations and its relations with number theory. The work has three objectives; first to construct motives for Hilbert modular forms of a particular weight, second to prove a conjecture relating the existence of Heisenberg models to the multiplicity pairing, and finally to construct a correspondence between certain representations of unitary groups with representations of the general linear group. This research is in a part of number theory generally known as the Langland's program. Number theory is the study of the properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished a driving force in creating new mathematics in other diverse parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus; it embodies the modern approach to the study of whole numbers. Modern number theory is very technical and deep, but it has had astonishing applications in areas like theoretical computer science and coding theory.

小行星9401466 该奖项资助乔纳森·罗加夫斯基教授在自守表示理论及其与数论关系方面的研究。 这项工作有三个目标; 第一，构造动机希尔伯特模形式的一个特定的重量，第二，证明一个猜想有关的存在海森伯模型的多重配对，最后，构建一个对应关系的某些表示酉群的代表一般线性群。 这项研究是数论的一部分，通常被称为朗兰纲领。 数论是研究整数的性质，是数学最古老的分支。从一开始，数论中的问题就为在这门学科的其他不同部分创造新的数学提供了动力。朗格兰纲领是一种将数论与微积分联系起来的一般哲学，它体现了研究整数的现代方法。 现代数论是非常技术性和深刻的，但它在理论计算机科学和编码理论等领域有着惊人的应用。