Automorphic L-functions and Sums of Automorphic L-functions

自同构 L 函数和自同构 L 函数之和

• 批准号: 9970118
• 负责人: Solomon Friedberg
• 金额: $ 11.15万
• 依托单位: Boston College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970118&HistoricalAwards=false
• 关键词: Automorphic; functions; Sums

9970118This project will study L-functions, which arise in number theory, representation theory, and harmonic analysis. Specifically, the project will study automorphic L-functions through the systematic examination of certain Dirichlet series in two complex variables built up out of sums of L-functions. These naturally occurring Dirichlet series are not themselves Euler products, but their individual coefficients are Eulerian. The intent is to use the extra variable in these series to extract analytic information similar to that which one could be obtained by the approximate functional equation were it possible to carry it out to infinite length. These two variable Dirichlet series originally appeared in investigations of Rankin-Selberg integrals. This project will also continue the study these integrals.In the last part of the twentieth century, the arithmetic properties of the integers have found new application in communications, security and other surprising areas of modern life. Mathematicians have long studied the integers in a branch of mathematics called number theory. Some of the simplest properties of the integers still contain deep mysteries, and recently mathematicians have developed powerful new techniques to explore these mysteries. The broad aim of this project is to study functions which exhibit certain complicated symmetries. These functions are of interest because they often encode arithmetic information about other things, for instance the number of solutions to sets of equations. The study of these functions provides insight into the symmetries and into the encoded arithmetic.

9970118这个项目将研究L功能，该功能是在数字理论，表示理论和谐波分析中出现的。 具体而言，该项目将通过对某些Dirichlet系列的系统检查中的两个复杂变量来研究自动L功能。 这些天然发生的迪里奇系列本身并不是欧拉产品，但它们的个体系数是欧拉尔的。 目的是使用这些系列中的额外变量来提取类似于通过近似功能方程获得的分析信息，如果可以将其执行到无限长度。 这两个可变的Dirichlet系列最初出现在Rankin-Selberg积分的研究中。 该项目还将继续研究这些积分。在20世纪的最后一部分，整数的算术属性在通信，安全和其他现代生活的其他令人惊讶的领域中找到了新的应用。 数学家长期以来一直在数学分支中研究数字理论的整数。 整数的一些最简单的特性仍然包含深度的奥秘，最近数学家开发了强大的新技术来探索这些谜团。 该项目的广泛目的是研究表现出某些复杂对称性的功能。 这些功能引起了人们的关注，因为它们通常编码有关其他事物的算术信息，例如方程组集的解决方案数量。 这些功能的研究提供了对对称性和编码算术的见解。