RUI: Automorphic Summation Formulae

RUI：自守求和公式

• 批准号: 0502730
• 负责人: Jennifer Beineke
• 金额: --
• 依托单位: Western New England University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0502730&HistoricalAwards=false
• 关键词: RUI; Automorphic; Summation; Formulae

This project explores the relationship between moments of the Riemann zeta function and automorphic forms. Motivated by recent conjectures on the moments, Professor Beineke plans to continue development of a new class of automorphic summation formulae in order to establish connections between the 2k-th moment of the Riemann zeta function and Eisenstein series on GL(2k). Initial results in the case where k = 1 have been developed by Professor Beineke in collaboration with Professor Daniel Bump at Stanford University.This is a project in number theory, one of the oldest branches of mathematics. The foundations of number theory lie in the study of the positive integers and finding patterns in these integers. A function of interest in number theory, which may provide information about patterns of prime numbers, is the Riemann zeta function. Results about this function could have applications to cryptography and Internet security. Professor Beineke's project investigates other number-theoretic objects called automorphic forms, and their possible connections to average values of the Riemann zeta function. These connections were initially motivated by results stemming from Random Matrix Theory, a subject originally used to develop models in experimental physics.

这个项目探讨了黎曼zeta函数的矩和自守形式之间的关系。 受最近关于矩的研究的启发，Beineke教授计划继续开发一类新的自守求和公式，以建立黎曼zeta函数的2k阶矩与GL（2k）上的爱森斯坦级数之间的联系。 在k = 1的情况下，Beineke教授与斯坦福大学的丹尼尔·邦普教授合作得出了初步结果。这是数论中的一个项目，数论是数学中最古老的分支之一。 数论的基础在于对正整数的研究，并在这些整数中找到模式。 数论中一个有趣的函数是黎曼zeta函数，它可以提供有关素数模式的信息。 该函数的相关结果可应用于密码学和网络安全。 Beineke教授的项目研究了其他称为自守形式的数论对象，以及它们与黎曼zeta函数平均值的可能联系。 这些联系最初是由随机矩阵理论的结果驱动的，随机矩阵理论最初是用于开发实验物理模型的学科。