Mathematical Sciences: Arithmetic of Automorphic Forms

数学科学：自守形式的算术

• 批准号: 8700798
• 负责人: Paul Garrett
• 金额: $ 3.65万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700798&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Automorphic; Forms

This research will concentrate on an investigation of integral representations of Dirichlet series, L-functions, automorphic forms and related objects. The kernels of interest for the integral representations are Eisenstein series on reductive algebraic groups or some suitable "fragments" of such Eisenstein series. Results on the nature of special values, analytic continuations and functional equations would follow from the existence of such integral representations. This research will focus on various analytic functions that encode important number theoretic information. This technique allows one to apply the deep results of analysis to obtain number theoretic information. A basic analytic tool is to represent these functions as integrals of functions which are better understood. That is precisely what the P.I. intends to do and has done so successfully in the past.

这项研究将集中在调查 Dirichlet级数的积分表示，L-函数， 自守形式和相关对象。 利益核心 对于积分表示是Eisenstein级数， 约化代数群或这种约化代数群的一些合适的“片段”， 爱森斯坦级数。 关于特殊值性质的结果， 解析延拓和函数方程可以从 这种积分表示的存在性。 这项研究将集中在各种分析功能， 编码重要的数论信息。 这种技术 允许一个人应用分析的深度结果来获得数字 理论信息 一个基本的分析工具是表示 这些函数作为函数的积分， 明白 这正是私家侦探。打算这样做， 在过去取得了成功。