论文标题
Riemann Zeta功能的非平凡零的分布
The Distribution of the Nontrivial Zeros of Riemann Zeta Function
论文作者
论文摘要
对于足够大的$ t $，我们改进了Riemann Zeta函数非平凡零零$ζ（σ+IT）$的分布的估计，这是基于对沿良好选择的轮廓的某些特殊对数$ζ$ζ（σ+IT）的特殊对数积分的精确计算。选择一个特殊和单值的坐标转换$ s =τ（z）$作为$ z =χ（s）$的倒数，功能方程$ζ（s）=χ（s）ζ（1-s）$被简化为$ g（z）= z \，g _--（g _--（q _--（Q _-）） $ g（z）=ζ（s）=ζ\circτ（z）$和$ g _- $是$ g $的共轭分支。指定了两种类型的特殊和对称轮廓$ \ partiald_ε^1 $和$ \ $ \ a部分d_ε^2 $在$ s $坐标中指定，并且不当的对乘$ζ$的对数$ζ$的对数积分不当，$ \ \ \ \ \ partiald_ε^1 $ and $ \ paintiald_ε^2 $在$ z =χ（s）$。对于足够大的$ t $的关键带中的任何域都可以由$d_ε^1 $或$d_ε^2 $涵盖，以及最终揭示了$ζ（S）$的非平凡零的分布，这比Riemann的初始假设和Rhythm更为微妙，并且与$ up的参数相比，$ c（$ c）$ c（$ c）（\ freac $ c）。
We improve the estimation of the distribution of the nontrivial zeros of Riemann zeta function $ζ(σ+it)$ for sufficiently large $t$, which is based on an exact calculation of some special logarithmic integrals of nonvanishing $ζ(σ+it)$ along well-chosen contours. A special and single-valued coordinate transformation $s=τ(z)$ is chosen as the inverse of $z=χ(s)$, and the functional equation $ζ(s) = χ(s)ζ(1-s)$ is simplified as $G(z) = z\, G_-(\frac{1}{z})$ in the $z$ coordinate, where $G(z)=ζ(s)=ζ\circτ(z)$ and $G_-$ is the conjugated branch of $G$. Two types of special and symmetric contours $\partial D_ε^1$ and $\partial D_ε^2$ in the $s$ coordinate are specified, and improper logarithmic integrals of nonvanishing $ζ(s)$ along $\partial D_ε^1$ and $\partial D_ε^2$ can be calculated as $2πi$ and $0$ respectively, depending on the total increase in the argument of $z=χ(s)$. Any domains in the critical strip for sufficiently large $t$ can be covered by the domains $D_ε^1$ or $D_ε^2$, and the distribution of nontrivial zeros of $ζ(s)$ is revealed in the end, which is more subtle than Riemann's initial hypothesis and in rhythm with the argument of $χ(\frac{1}{2}+it)$.
