Riemann zeta function and quantum theory

- This article was written long time ago. For more accurate article, refer to article 30 - $\gamma(z)$ can be defined like this. (1) $\Gamma(z)=(z-1)!=\gamma(z)+m, m$: integer. $\gamma(z)=(z-1)!-m$ The reason that $m$ is added is to divide into integer part and $\gamma(z)$ whose real part is less than $1$. Using the relation $z-n=(-1)^{n+1}\cos^{n+1}\frac{\pi (z-n+1)}{2((z-n)!+1)}$, wh..

According to Lorentz effect in the gravitational field, (1) $2GM_N/r_Nc^2=2f(N)=\pi((N-1)!+1)/N$ (=$N\pi$ when they are scattered) In pure gravitational field, there is the relation like this, $GM/rc^2=1/\beta$. From (1), $\beta=rc^2/GM \approx 2N/\pi((N-1)!+1) \leq 2/\pi$, $(N=2)$ This is because there is a minimum length $r_h$ and when external conditions are same, mass (or density) is not dir..