Definition:Riemann Zeta Function/Critical Line

Definition
Consider the Riemann zeta function $\map \zeta s$.

Let $s = \sigma + i t$.

The line defined by the equation $\sigma = \dfrac 1 2$ is known as the critical line.

Hence the popular form of the statement of the Riemann Hypothesis:
 * All the nontrivial zeroes of the Riemann zeta function lie on the critical line.


 * Critical-Strip.png

Also see

 * Riemann Hypothesis


 * Definition:Critical Strip