The line ℜ[s] = 1/2 in the complex plane on which the Riemann hypothesis asserts that all nontrivial (complex) Riemann zeta function zeros lie. The plot above shows the first few zeros of the Riemann zeta function, with the critical line shown in red. The zeros with ℑ[s] = 0 and ℜ[s]<0 that do not line on the critical line are the trivial zeros of ζ(s) at s = - 2, -4, .... Although it is known that an infinite number of zeros lie on the critical line and that these comprise at least 40% of all zeros, the Riemann hypothesis is still unproven. An attractive poster plotting the Riemann zeta function zeros on the critical line together with annotations for relevant historical information, illustrated above, was created by Wolfram Research.

critical strip | Riemann hypothesis | Riemann zeta function | Riemann zeta function zeros