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教授在自守形式和表示理论方面的研究。这项工作涉及三个问题的关系，数论，其中有L-功能作为一个共同的主题。本文主要讨论了特殊线性群SL（2）上尖点型空间重数为1的证明程序。第二个问题涉及一般线性群GL（n）的强重数1定理的精细形式。最后，主要研究人员试图完成证明泰特猜想的所有四元数志村表面。 从历史上看，自守形式产生于世纪中期的非欧几里德几何。因此，数学家和物理学家早就认识到，许多具有根本重要性的对象在其基本性质上是非欧几里德的。这一领域主要关注的是关于整数的问题，但在几何和分析的应用中，它保留了与其历史根源的联系，从而与理论物理中的规范理论和信息论中的编码理论等不同领域的问题保持联系。