论文标题
Riemann Zeta功能的素数和非平凡零的复发公式
The recurrence formulas for primes and non-trivial zeros of the Riemann zeta function
论文作者
论文摘要
在本文中，我们从素数和非平凡零的角度探讨了Riemann Zeta功能。我们开发了$ n $ th+1 prime的Golomb的复发公式，假设（RH），我们为Riemann Zeta函数的$ n $ th+1非平凡零提出了一个分析复发公式。因此，必须知道所有非平凡的零零，以生成$ n $ th+1的非平凡零。我们还基于Prime Zeta函数探讨了素的复发公式的变化，这将是基于次级Zeta函数的非平凡零零复发公式的基础。在最后一部分中，我们回顾了提出的公式，并概述了素数和非平凡零之间的二元性。所提出的公式意味着所有素数可以转换为单个的非平凡零（假设RH），相反，所有非平凡的零可以转换为单个素数（不是假设RH）。同样，在本文中，我们总结了数值计算并验证提出的结果以高精度。
In this article, we explore the Riemann zeta function with a perspective on primes and non-trivial zeros. We develop the Golomb's recurrence formula for the $n$th+1 prime, and assuming (RH), we propose an analytical recurrence formula for the $n$th+1 non-trivial zero of the Riemann zeta function. Thus all non-trivial zeros up the $n$th order must be known to generate the $n$th+1 non-trivial zero. We also explore a variation of the recurrence formulas for primes based on the prime zeta function, which will be a basis for the development of the recurrence formulas for non-trivial zeros based on the secondary zeta function. In the last part, we review the presented formulas and outline the duality between primes and non-trivial zeros. The proposed formula implies that all primes can be converted into an individual non-trivial zero (assuming RH), and conversely, all non-trivial zeros can be converted into an individual prime (not assuming RH). Also, throughout this article, we summarize numerical computation and verify the presented results to high precision.
