Is it true that $\left|\frac{\zeta(0.5+it) }{\zeta(0.5-it)}\right|\leq 1 $, for $t\in \mathbb{R} $?

Question

I'm interested one Bounds values of Riemann zeta function on critical line , really i have got this from some computation I did in wolfram alpha for some values of $t$ and according to the studying number of solution of : $\zeta(0.5+it )= z$ , for every real $t$ and $z \in \mathbb{C}$ this Bounds :

$$\left|\frac{\zeta(0.5+it) }{\zeta(0.5-it)}\right|\leq 1 $$

Now if we assume RH Holds the inequality is become an equality to $1$ by passage of limit and it is true if $(t=0)$ , But what about $t \neq 0$ ?

Answer 1

Any meromorphic function $f$ real-valued on the real line has the property that $f(\overline s)=\overline{f(s)}$, so the absolute values are identical. It's nothing special to zeta.