关于黎曼ζ函数的II部分

Almost all of the nontrivial zeros of the Riemann zeta-function are on the critical line

Applying Littlewood's lemma in connection to Riemann's Hypothesis and exploiting the symmetry of Riemann's $xi$ function we show that almost all nontrivial Riemann's Zeta zeros are on the critical line.

Zeros of the Riemann Zeta Function

In this paper, we present a proof of the Riemann hypothesis. We show that zeros of the Riemann zeta function should be on the line with the real value 1/2, in the region where the real part of complex variable is between 0 and 1.

与狄利克雷ζ函数相关的某些级数与广义黎曼假设

Some Series Related to Extended Riemann Hypothesis for Dedekind Zeta Functions

本文在广义黎曼假设下，推导了与狄利克雷ζ函数相关的级数闭式，并证明闭式成立则所有高零点位于临界线，从而获得黎曼假设的等价陈述。

On zeros of the Riemann zeta function

This paper shows that, in the critical strip, the Riemann zeta function $ζ(s)$ have the same set of zeros as $F(s):=\int_0^\infty t^{s-1}(e^t+1)^{-1}dt$, and then discusses the behavior of $F(s)$.

黎曼ζ函数的一个定性性质

A Qualitative Property of the Riemann zeta function

论文被作者撤回。它包含各种错误。

Dedekind zetas和Dirichlet L-函数的广义黎曼假设的证明

Proof of generalized Riemann hypothesis for Dedekind zetas and Dirichlet L-functions

在Hecke证明$ζ_{k}$的函数方程和[ $M_{A}$ ]（黎曼假设的代数证明）中证明黎曼假设的方法的基础上，给出了代数数域$k$ -的zeta函数$ζ_{k}$的广义黎曼假设（简称gRH）的一个简短证明. Dirichlet L-函数的广义黎曼假设是$ζ_{k}$的（gRH）和连接Dedekind zeta与L-函数的适当乘积公式的直接结果。

La Zeta de Riemann est irrationnelle aux impairs positifs

We found, by Hurwitz's Zeta Function, a new functional equation for Riemann Zeta Function. Considering this equation for $s=2$ and $s=1$, we determine a relation between the values of Riemann zeta Function on positive integers. The Matrix has two dimensions, and the second member is the vector (1, $-ζ(2)$). The elements of this vector are linearly independent on the Rationals; and from this independence, we determined that $ζ(j)$ is irrational for each j=3,4,5,6,7,8,9,....

周期问题：黎曼ζ函数零点的有趣周期性

The cycle problem: an intriguing periodicity to the zeros of the Riemann zeta function

对n^rho的对数积分的实部值求和，其中rho是黎曼ζ函数的连续零点系列之一，揭示了总和的意外周期性。这就是周期问题。

黎曼ζ函数$ζ$的所有非平凡零点$ρ$满足的方程

An equation satisfied by all non-trivial zeros $ρ$ of the Riemann zeta function $ζ$

证明了如果$ρ$是黎曼ζ函数$ζ$的非平凡零点，则$$2^ρ+ \frac{1}{ρ- 1} + 1/2 = ρ\int_{1}^{\infty} {t + 1/2} t^{-ρ-1} dt$$，其中，${x}$是$x$的分数部分.

黎曼ζ函数的递推关系和函数方程

Recursion Relations and Functional Equations for the Riemann Zeta Function

引入了黎曼ζ函数的新的递推关系。它们的推导是从标准的函数方程开始的。新的函数方程具有实增量和虚增量两种形式，可应用于整个复平面。我们已经开发了各种版本的递归关系消除每个系数函数，留下平原zeta函数

Notes on the Zeros of Riemann's Zeta Function

The functional equation for Riemann's Zeta function is studied, from which it is shown why all of the non-trivial, full-zeros of the Zeta function $ζ(s)$ will only occur on the critical line {$σ=1/2$} where {$s=σ+I ρ$}, thereby establishing the truth of Riemann's hypothesis. Further, two relatively simple transcendental equations are obtained; the numerical solution of these equations locates all of the zeros of {$ζ(s)$} on the critical line.

关于黎曼ζ函数及另一个密切相关的无穷级数在自然数处取值的初等方法

On Elementary Methods To Evaluate Values of The Riemann Zeta Function and Another Closely Related Infinite Series At Natural Numbers

本文给出了求黎曼ζ函数在自然数为偶数时的值以及求一个密切相关的级数在自然数为奇数时的值的一种初等方法。还介绍了另一种方法，特别是用于评价$ζ(2),$。

黎曼ζ函数的零点与伪随机到调和行为的转变

The zeros of the Riemann-zeta function and the transition from pseudo-random to harmonic behavior

本文基于黎曼ζ函数的非平凡零点，提出了一种新的函数。这样的函数表现出一个有趣的行为：当函数的自变量增加时，它从伪随机行为变为频率降低的谐波行为。