Mathematical Sciences: New Models in the Rankin-Selberg Method and Uses of the Metaplectic Group

数学科学：Rankin-Selberg 方法的新模型和 Metaplectic 群的使用

• 批准号: 9023441
• 负责人: Daniel Bump
• 金额: $ 21.71万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-15 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9023441&HistoricalAwards=false
• 关键词: Mathematical; Sciences; New; Models; Rankin

This award supports the research of Professor D. Bump to work in automorphic functions. He intends to work on extending the Rankin Selberg method and on new uses of the metaplectic group. These include the study of non-unique Whittaker models of theta functions on the n-fold cover of GL(2). Modular forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.

该奖项支持D教授的研究。凸块至 在自守函数中工作。 他打算努力扩大 兰金Selberg方法和元代数的新用途 组 这些研究包括非唯一的Whittaker模型， 在GL（2）的n重覆盖上的theta函数。 模形式起源于非欧几何， 世纪中期。 数学家和 物理学家早就意识到， 基本的重要性是非欧几里德在其基本性质。 此字段主要涉及有关 整数，但在其使用的几何和分析，它 保留了与其历史根源的联系，从而与问题 从理论物理中的规范理论， 信息论中的编码理论