Mathematical Sciences: Multiplicity One Results for Automorphic Forms via L-functions

数学科学：通过 L 函数得出自同构形式的重数一结果

• 批准号: 9501151
• 负责人: Dinakar Ramakrishnan
• 金额: $ 9.45万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1998-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501151&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multiplicity; Results; Automorphic

This award supports the research of Professor Dinakar Ramakrishnan in the theory of automorphic forms and representations. This work involves three problems with relations to number theory, which have L-functions as a common theme. The main focus is on a program to prove multiplicity one for the space of cusp forms on the special linear group SL(2). The second problem concerns fine versions of the strong multiplicity one theorem for the general linear group GL(n). Finally, the principal investigator seeks to complete a proof of the Tate conjecture for all quaternionic Shimura surfaces. Historically, automorphic 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Dinakar Ramakrishnan教授在汽车形式和代表理论方面的研究。这项工作涉及与数字理论关系的三个问题，这些问题以L功能为共同的主题。主要的重点是在特殊线性组SL（2）上证明尖峰形式空间的多样性一个程序。第二个问题涉及一般线性组GL（n）的强多重性一个定理的精细版本。最后，首席研究人员试图完成所有Quaternionic Shimura表面的泰特猜想的证明。 从历史上看，十九世纪中叶的非欧几里得几何形状产生了自动形式。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。