The Graph of the Riemann zeta function ζ(s)

The Riemann zeta function, in symbols ζ(s), is a rather complicated function which Bernhard Riemann (18261866) introduced in 1859 to generalize the Euler zeta function
ζ(s)  = 
 n^{s}  (s > 1) 
to the complex plane. Since the Riemann zeta function ζ is a function from the complex plane C to itself, i.e., ζ: C > C, its graph cannot be represented as a 3D image. Instead, the real part and the imaginary part are plotted separately. In addition, the absolute value ζ(s) may be shown.
You can adjust the ranges of the plotted x, y, and z values, where s = x + iy, and z = Re ζ(s), z = Im ζ(s), or z = ζ(s), respectively.
In the plot, the real and imaginary lines are projected on the graph and are marked red. The socalled "critical line" (Re s = 1/2) is marked green; the famous Riemann hypothesis conjectures that all zeros besides s = 2, 4, 6, .... lie on the critical line.
© de Vries 2004 