Mathematical Sciences: "The Convergence of Euler Products"

数学科学：《欧拉积的收敛性》

• 批准号: 9103933
• 负责人: Louis de Branges
• 金额: $ 5.75万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-05-01 至 1993-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103933&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Convergence; Euler; Products

The matrix generalization of the Euler product has been introduced in previous work, and it has been shown that the Riemann Hypothesis is equivalent to the convergence question for related products of Moebius transformations. The present project is an estimation theory of such products which would be sufficient to answer the question posed by Riemann. In order to accomplish this it is proposed to construct disks that are mapped into each other by successive Moebius transformations of the matrix product. The solution of the Riemann Hypothesis is indeed the Holy Grail of analysis, and the principal investigator is by most accounts the most capable person in the world to attempt a solution. Even if a complete resolution does not result from this work the results that are obtained will be of tremendous value.

欧拉积的矩阵推广已经被 在以前的工作中引入，并且已经表明， 黎曼猜想等价于收敛问题 Moebius变换的相关产物。 本 项目是这样的产品的估计理论， 这足以回答黎曼提出的问题。 为了 为了实现这一点，建议构造 通过连续的Moebius变换映射到彼此， 矩阵产品。 黎曼猜想的解确实是神圣的 分析的圣杯，和主要研究者是由大多数 认为世界上最有能力尝试的人 一个解决方案 即使没有完全解决， 这项工作将取得巨大的成果 值