Critical line
Analysis
The vertical line in the complex plane consisting of numbers with real part 1/2, on which the Riemann hypothesis asserts all nontrivial zeta zeros lie.
What is usually left out
It is distinguished by the functional equation, which relates ζ(s) to ζ(1 − s) and so reflects the plane about this line. Hardy proved in 1914 that infinitely many zeros lie on it; that is compatible with infinitely many lying off it, which is why the result does not settle the hypothesis.
Related terms
In the atlas
- Riemann hypothesis — Number theory, open