Riemann Zeta Function Zeros
Visualizing ζ(s) in the complex plane — all known non-trivial zeros lie on Re(s) = 1/2
Controls
t range start:
0
t range:
50
Terms in sum:
30
Color scheme:
Phase (hue = arg)
Magnitude
Real part
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Known zeros on Re(s)=½:
The
Riemann Hypothesis
(1859): all non-trivial zeros of ζ(s) lie on the critical line Re(s) = ½.
Vertical dashed line = critical line. Dots = known zeros.
Color shows |ζ(s)| or phase arg(ζ(s)).
ζ(s) = Σ n^−s for Re(s)>1, analytically continued elsewhere.