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该项目将研究数论、表示论和调和分析中出现的 L 函数。 具体来说，该项目将通过系统检查由 L 函数之和构建的两个复变量中的某些狄利克雷级数来研究自同构 L 函数。 这些自然产生的狄利克雷级数本身并不是欧拉积，但它们的各个系数是欧拉的。 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函数方程（如果可以将其执行到无限长度）可以获得的分析信息。 这两个变量狄利克雷级数最初出现在Rankin-Selberg积分的研究中。 该项目还将继续研究这些积分。在二十世纪后半叶，整数的算术性质在通信、安全和现代生活中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称为数论的数学分支中研究整数。 整数的一些最简单的属性仍然包含着深刻的奥秘，最近数学家们开发了强大的新技术来探索这些奥秘。 该项目的主要目标是研究表现出某些复杂对称性的函数。 这些函数很有趣，因为它们通常对其他事物的算术信息进行编码，例如方程组的解的数量。 对这些函数的研究可以深入了解对称性和编码算术。