# Definition:Riemann Zeta Function/Critical Line

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## 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.