A complete Riemann zeta distribution and the Riemann hypothesis

Takashi Nakamura

Let $\sigma ,t\in \mathbb{R}$, $s=\sigma +\mathrm{i}t$, $\Gamma (s)$ be the Gamma function, $\zeta (s)$ be the Riemann zeta function and $\xi (s):=s(s-1){\pi }^{-s/2}\Gamma (s/2)\zeta (s)$ be the complete Riemann zeta fun…