论文标题
临界条右侧的Riemann Zeta函数的涡流状行为
The vortex-like behavior of the Riemann zeta function to the right of the critical strip
论文作者
论文摘要
基于最近在指数总和上建立的等价关系，在本文中，我们研究了与riemann zeta函数等效的函数类别中的一类函数。与此类函数有关，我们首先确定最大横坐标的值，其中任何函数的图像都无法采用前缀的参数。主要结果表明，这些函数实验中的每一个都像涡流一样，其图像的主要参数在垂直线$ \ operatatorName {re} s = 1 $附近无限期变化。特别是，关于riemann zeta函数$ζ$，对于每$σ_0> 1 $，我们可以确保存在相对密集的实数$ \ {t_m \} _ {m \ geq 1} $ $（\ operatorName {re}（ζ（σ+it_m）），\ operatorAtorName {im}（ζ（σ+it_m）））$，带有$σ\ in（1，σ_0）$，使前缀有限的有限数围绕着来源。
Based on an equivalence relation that was established recently on exponential sums, in this paper we study the class of functions that are equivalent to the Riemann zeta function in the half-strip $\{s\in\mathbb{C}:\operatorname{Re}s>1\}$. In connection with this class of functions, we first determine the value of the maximum abscissa from which the images of any function in it cannot take a prefixed argument. The main result shows that each of these functions experiments a vortex-like behavior in the sense that the main argument of its images varies indefinitely near the vertical line $\operatorname{Re}s=1$. In particular, regarding the Riemann zeta function $ζ(s)$, for every $σ_0>1$ we can assure the existence of a relatively dense set of real numbers $\{t_m\}_{m\geq 1}$ such that the parametrized curve traced by the points $(\operatorname{Re}(ζ(σ+it_m)),\operatorname{Im}(ζ(σ+it_m)))$, with $σ\in(1,σ_0)$, makes a prefixed finite number of turns around the origin.
