Nontrivial zero of the Riemann zeta function

A nontrivial zero of the Riemann zeta function lies in the critical strip $0<\Re s<1$. The Functional equation of the Riemann zeta function reflects such zeros across the critical line $\Re s=1/2$.

The critical strip for the Riemann zeta function is $0<\Re s<1$.

The critical line is the symmetry line $\Re s=1/2$ inside the critical strip.

The Riemann hypothesis asserts that every Nontrivial zero of the Riemann zeta function lies on the critical line $\Re s=1/2$.

The classical zero-free region asserts that for some $c>0$,Together with bounds for the logarithmic derivative, it permits contour arguments with exponentially small errors in $\sqrt{\log x}$.