Riemann Zeta Function

Critical strip, non-trivial zeros, and ζ(s) trajectory

Critical strip (s-plane)

ζ(s) output (w-plane)

Im(s) sweep: σ (Re): 0.50 Speed:

Known non-trivial zeros on critical line (Im): 14.135, 21.022, 25.011, 30.425, 32.935, 37.586, 40.919, 43.327

The Riemann Hypothesis conjectures all non-trivial zeros lie on Re(s)=½ (the critical line, shown in gold). The left panel shows the path through the critical strip; the right panel traces ζ(s) in the output plane. Each time the output spiral crosses the origin, a non-trivial zero occurs.