I was wondering if it was known whether there was some $ \frac{1}{2}<a<1$ and a $c>0$ such that $|\zeta (a+it)| \geq c$ for all $t \in \mathbb{R}$? That is, does anyone know of any literature proving the existence/nonexistence of a vertical line in the critical strip with $\zeta (s)$ bounded below by a constant?
I couldn't find anything online, but I could be looking in the wrong places or this could be completely trivial and I just don't know it. Either way, I'd appreciate if someone could point me in the right direction.