论文标题
Riemann Zeta功能的非平凡零的分析复发公式
Analytical recurrence formulas for non-trivial zeros of the Riemann zeta function
论文作者
论文摘要
在本文中，我们开发了四种类型的分析复发公式，用于假设（RH）在临界线上的Riemann Zeta函数的非平凡零。因此，为了生成$ n $ th+1的非平凡零，必须知道所有直至$ n $ th订单的零零。所有提出的公式均基于次级Zeta函数家族的某些闭合形式表示，这些Zeta函数家族已经在文献中可用。我们还提出了一个直接从素数生成非平凡零的公式。因此，所有素数都可以转换为单个的非平凡零，我们还提供了一组公式，将所有非平凡的零转换为单个素数。我们还将提出的结果扩展到其他Dirichlet-L函数，特别是，我们为Dirichlet Beta函数的非平凡零开发了一个分析复发公式。在本文中，我们还从数值上计算出这些公式的高精度，并回顾了计算的结果。
In this article, we develop four types of analytical recurrence formulas for non-trivial zeros of the Riemann zeta function on critical line assuming (RH). Thus, all non-trivial zeros up to the $n$th order must be known in order to generate the $n$th+1 non-trivial zero. All the presented formulas are based on certain closed-form representations of the secondary zeta function family, which are already available in the literature. We also present a formula to generate the non-trivial zeros directly from primes. Thus all primes can be converted into an individual non-trivial zero, and we also give a set of formulas to convert all non-trivial zeros into an individual prime. We also extend the presented results to other Dirichlet-L functions, and in particular, we develop an analytical recurrence formula for non-trivial zeros of the Dirichlet beta function. Throughout this article, we also numerically compute these formulas to high precision for various test cases and review the computed results.
