This question is asked based on curiosity. I came across few papers which find extreme values of RZF: $|\zeta(s)|$ on the critical line $Re(s)=\frac{1}{2}$. Though it is quite unclear whether it has got some scope.
When we are already striving to know whether the zeros lie elsewhere in the critical strip, few top mathematicians are trying to unravel the properties only on the critical line. Is it possible that the values or the growth of the function on the critical line definitely could lead us somewhere more exciting?
Thank you.