The Rankin-Selberg Method, Zeros of Special Functions and Models of Representations Over Finite Fields

Rankin-Selberg 方法、特殊函数的零点和有限域上的表示模型

• 批准号: 9622819
• 负责人: Daniel Bump
• 金额: $ 20.24万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622819&HistoricalAwards=false
• 关键词: Rankin; Selberg; Method; Zeros; Special

This award provides funding for the investigator's continued research into the Rankin-Selberg method. Much of this work will likely be joint work. The research will likely shift from the search for new Rankin-Selberg integrals to extracting more information from existing Rankin-Selberg constructions. An initial problem will be the nonvanishing of the archimedean local integrals for the symmetric cube L-functions on GL(2). Friedberg, Hoffstein, and Bump have been exploring reflection groups coming from double Dirichlet series with automorphic L-functions on GL(n) and quadratic characters. The corresponding question for GL(2) and cubic characters will be studied. Other problems on automorphic forms will be investigated. This research falls into the general mathematical field of Number Theory. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.

该奖项为研究人员继续研究Rankin-Selberg方法提供资金。这项工作的大部分可能是联合工作。研究可能会从寻找新的Rankin-Selberg积分转向从现有的Rankin-Selberg结构中提取更多信息。初始问题是GL（2）上对称立方L-函数的阿基米德局部积分的非零性。Friedberg、Hoffstein和Bump一直在研究GL（n）上具有自守L-函数和二次特征标的二重Dirichlet级数的反射群。我们将研究GL（2）和三次特征标的相应问题。自守形式的其他问题将被研究。 本文的研究属于数论中的一般数学领域福尔斯。 数论有其历史根源，在研究整个数字，解决这样的问题，如那些处理整除一个整数由另一个。它是数学中最古老的分支之一，几个世纪以来，人们纯粹出于美学的原因而追求它。然而，在过去的半个世纪，它已成为一个不可或缺的工具，在各种 在诸如数据传输和处理以及通信系统的领域中的应用。