From the previous article1, $\zeta_e(s, x)$ can be wirtten like belows. (1) $\zeta_e(s, x)=\frac{q(x)(1-x^{s})}{(e^{i\pi p(x)}- 1)(1+ g_{s}(x))}$ $=\frac{x^s-1}{e^{i\pi p(x)}- 1}h_s(x)$ To make the integral form of zeta function more generally, assuming $i\pi p(x)$->$i\pi(p(x)-n), n:$ integer, this equation can be modified like belows. (2) $\zeta_e(s, x)=\frac{(x^s-1)h_s(x)}{e^{i\pi(p(x)-n)..
