Contour Plots of the Zeta Function

y

50

Δy

20

The level curves at zero of the real and imaginary parts of the Riemann zeta function show their intersections on the real line

s=1/2+yi

from

y

to

y+Δy

. The Riemann Hypothesis states that all of the zeros (other than those at the even negative integers) occur on this critical line.