论文标题
生成Riemann Zeta功能和Dirichlet L功能的动态系统框架
A Dynamical Systems Framework for Generating the Riemann Zeta Function and Dirichlet L-functions
论文作者
论文摘要
我们首先构建了一个动力学系统模型，该模型在整个关键带上是完整的Riemann Zeta功能的分析延续。所得的数学构建体涉及两个对称发生器函数的线性插值，可用于推断Riemann Zeta函数的非平凡零的全局性质，使用浓度界限。因此，提出的动态系统框架提供了一种研究著名的Riemann假设的替代方法，该假设在本文中几乎肯定是正确的。我们还表明，该框架足以研究Dirichlet L功能的非平凡零，在本文中，我们表明，在特定条件下，广义的Riemann假设几乎肯定是正确的。
We first construct a dynamical systems model which in its steady-state serves as an analytic continuation of the completed Riemann zeta function over the entire critical strip. The resulting mathematical construct involves a linear interpolation of two symmetric generator functions which can be used to infer the global properties of the non-trivial zeros of the Riemann zeta function using concentration bounds. The proposed dynamical systems framework thus provides an alternative method for investigating the celebrated Riemann Hypothesis which is shown in this paper to be almost surely true. We also show that the framework is general enough to study the non-trivial zeros of the Dirichlet L-functions and in this paper we show that under specific conditions, the generalized Riemann Hypothesis is also almost surely true.
