标题： 黎曼辅助函数的无穷乘积 显示英文标题

标题： Infinite Product of the Riemann auxiliary function

摘要： 我们得到辅助函数$\mathop{\mathcal R}(s)$的乘积，并研究其在临界线上作为相位的$\omega(t)$相关函数。 函数$\omega(t)$确定了$\zeta(s)$在临界线上的零点。 我们研究了$\mathop{\mathcal R}(s)$的零点对$\omega(t)$的影响。 因此，$\mathop{\mathcal R}(s)$的零点与$\zeta(s)$的零点之间的关系得以确定。 显示英文摘要

摘要： We obtain the product for the auxiliary function $\mathop{\mathcal R}(s)$ and study some related functions as its phase $\omega(t)$ at the critical line. The function $\omega(t)$ determines the zeros of $\zeta(s)$ on the critical line. We study the influence of the zeros of $\mathop{\mathcal R}(s)$ on $\omega(t)$. Thus, the relationship between the zeros of $\mathop{\mathcal R}(s)$ and those of $\zeta(s)$ is determined.