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.
Also see
Sources
- Weisstein, Eric W. "Critical Line." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CriticalLine.html