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.

9401466 Rogawski该奖项为乔纳森·罗戈斯基（Jonathan Rogawski）教授的调查提供了资金，该奖项在汽车代表理论及其与数字理论的关系中资助。 这项工作有三个目标； 首先要为特定权重的希尔伯特模块化形式构建动机，其次是证明一个猜想，将海森伯格模型的存在与多重性配对有关，最后是在单一组的某些表示与通用线性组表示之间构建对应关系。 这项研究是数字理论的一部分，通常称为兰兰的计划。 数字理论是对整数的性质的研究，是数学最古老的分支。从一开始，理论的问题就为在学科的其他不同部分创建新数学方面提供了一种驱动力。兰兰（Langland）的计划是将数字理论与演算联系起来的一般哲学。 它体现了整个数字研究的现代方法。 现代数字理论非常技术性和深刻，但在理论计算机科学和编码理论等领域中具有惊人的应用。