Infinite Product of the Riemann auxiliary function

Abstract

We obtain the product for the auxiliary function $\mathcal{R}(s)$ 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 $\mathcal{R}(s)$ on $\omega (t)$. Thus, the relationship between the zeros of $\mathcal{R}(s)$ and those of $\zeta (s)$ is determined.

arXiv comment12 pages