Asymmetry for the Riemann Hypothesis

In this manuscript, we show that the Riemann zeta function satisfies $(\zeta (s),\zeta (1-\bar{s}))\mathrm{\ne }(0,0)$ for any $s$ in the critical strip, except on the critical line. This still holds even when the fractional part function is replaced by a function satisfying a specific “Rotation Number Hypothesis”.