Mathematical Sciences: Theta Functions and Eisenstein Serieson the Metaplectic Group

数学科学：Theta 函数和爱森斯坦 Metaplectic 群系列

• 批准号: 9023202
• 负责人: Jeffrey Hoffstein
• 金额: $ 16.28万
• 依托单位: Brown 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: 1991-05-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9023202&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theta; Functions; Eisenstein

This award supports the research of Professor J. Hoffstein to work in automorphic functions. He intends to work on obtaining the symmetric cube L-series of a cusp form on GL(2) as a Rankin Selberg integral. He also intends to study 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J. Hoffstein教授的研究，从事汽车功能。 他打算致力于在GL（2）上以Rankin Selberg的整体形式获得对称立方体L系列的对称立方体L系列。 他还打算研究theta函数的非唯一Whittaker模型，该模型在GL（2）的N倍覆盖率上。 模块化形式是从19世纪中叶的非欧几里得几何形状产生的。 因此，数学家和物理学家长期以来都意识到，许多基本重要性的对象在基本本质上都是非欧国人。 该领域主要关注有关整数的问题，但是在使用几何和分析时，它保留了与其历史根源的联系，从而在信息理论中的理论物理学和编码理论中与量规理论等领域的问题保持联系。