Mathematical Sciences: "The Convergence of Euler Products"

欧拉乘积的矩阵推广在前人的工作中已经被介绍，并且证明了黎曼假设等价于Moebius变换的相关乘积的收敛问题。本项目是对这类产品的估计理论，足以回答Riemann提出的问题。为了实现这一点，提出了通过矩阵乘积的连续Moebius变换来构造相互映射的盘。黎曼假说的解决方案确实是分析的圣杯，而大多数人认为首席研究员是世界上最有能力尝试解决方案的人。即使这项工作没有产生一个完全的解决办法，所取得的结果也将具有巨大的价值。

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.