ζ(s) Explorer

s = 0.5 + 14.13i

ζ(s) = —

|ζ(s)| —

Near Zero? —

Riemann Zeta Function

The $1 million question: do all non-trivial zeros lie on the critical line Re(s) = ½?

History: Riemann's 1859 paper connected prime numbers to zeros of ζ(s). The hypothesis remains unproven after 165 years.

ζ(s) ≈ 0 + 0i

arg(ζ(s))

Im(s)