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Riemann Hypothesis

Statement

The Riemann hypothesis posits that the nontrivial zeros of the Riemann zeta function ζ(s) all lie on the critical line Re(s) = 1/2.

Formal statement

for all _(n, n element Z ∧ n!=0)Re(ρ_n) = 1/2

Alternate names

Hilbert's eighth problem | RH | Smale's first problem

History

formulation date | 1859 (166 years ago)
formulator | Bernhard Riemann
status | open

Associated equation

Re(ρ_n) = 1/2

Current evidence

It has been verified that the first 1×10^13 nontrivial zeros of the zeta function lie on the critical line.
Conrey (1989) proved that at least 40% of the nontrivial zeros of the zeta function lie on the critical line.

Associated prizes

prize offered for solution | $1 million "Millennium Prize Problem" of The Clay Mathematics Institute.

Classes

mathematical hypotheses | Millennium Prize problems | prize mathematics problems | Smale's problems | unsolved mathematics problems

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