$|\zeta(2+it)| >y(t)$?

Question

What is known about $|\zeta(2+it)| > y(t)$ where $t$ is real ?

It is clear that $|\zeta(2+it)|\neq 0$ and $|\zeta(2+it)|<\zeta(2)$ but do we have known sharp boundaries for this $y(t)$ ?

Answer 1

I guess you saw that $|\zeta(\sigma+it)| \ge \zeta(2\sigma)/\zeta(\sigma)$ is evident from the Euler products.

$$\inf_t |\zeta(\sigma+it)| = \zeta(2\sigma)/\zeta(\sigma)$$ needs using that the $\log p$ are $\Bbb{Q}$-linearly independent so for any $m$ you can find $t_m$ such that $|1-p^{-\sigma-it_m}| > 1+p^{-\sigma}-1/m$ for $p\le m$.