Mathematical Sciences: Rankin Selberg Integrals and Applications

数学科学：Rankin Selberg 积分及应用

• 批准号: 9103263
• 负责人: Stephen Rallis
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 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: 1991-06-01 至 1996-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103263&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Rankin; Selberg; Integrals

This award supports the research of Professor S. Rallis and Professor D. Ginzburg to work in automorphic functions. Professor Rallis intends to work on the relation of the Rankin Selberg integral representation of L functions to various problems in the theory of automorphic forms. Professor Ginzburg intends to work on applications of the Rankin Selberg method to Langland's conjecture. 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S.Rallis教授和D.Ginzburg教授在自同构函数方面的研究。Rallis教授打算研究L函数的Rankin Selberg积分表示与自同构形理论中的各种问题之间的关系。金兹伯格教授打算将兰金·塞尔伯格方法应用于朗兰德猜想。模形式起源于19世纪中叶的非欧几里德几何。因此，数学家和物理学家都早已认识到，许多具有根本重要性的物体本质上都是非欧几里得的。这个领域主要涉及关于整数的问题，但在使用几何和分析时，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有关。