Mathematical Sciences: Arithmetic of Automorphic Forms on GSp(4)

数学科学：GSp(4) 上的自同构算术

• 批准号: 8804527
• 负责人: Don Blasius
• 金额: $ 4.22万
• 依托单位: CUNY Baruch College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1990-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8804527&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Automorphic; Forms

This research is in the general area of the so-called Langlands Program, a subject that lies on the bridge between Number Theory and Representation Theory in Modern Analysis. More specifically one attaches an L-function to a cuspidal automorphic representation of the group of two by two matrices over the rational adele ring, and one also attaches an L-function to an irreducible representation of the galois group of the algebraic closure of the rational numbers. The main question to be investigated on this project is when these two L-function coincide. A new method has been devised to answer this question and this method will be pursued. Two different types of functions that contain a great deal of number theoretic information will be investigated. When they can be shown to coincide one can obtain much important arithmetic information about the more obscure one from the better understood one. Producing these formulas is the focus of this research.

这项研究属于所谓的朗兰兹纲领的一般领域，该纲领是现代分析中数论和表示论之间的桥梁。 更具体地说，将一个 L 函数附加到有理阿黛尔环上的二乘二矩阵的群的尖自同构表示上，并且还将一个 L 函数附加到有理数的代数闭包的伽罗瓦群的不可约表示上。 该项目要研究的主要问题是这两个 L 函数何时重合。 已经设计了一种新方法来回答这个问题，并且将继续采用这种方法。 将研究包含大量数论信息的两种不同类型的函数。 当它们能够被证明是一致的时，人们可以从更容易理解的信息中获得关于更模糊的信息的许多重要算术信息。 产生这些公式是本研究的重点。