Wolfram|Alpha

Computing...

Input interpretation:

Riemann hypothesis (mathematical problem)


Statement:

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


Formal statement:

(for all)_(n, n element Z && n!=0)Re(rho_n) = 1\/2


Alternate names:

Hilbert\'s eighth problem\nRH\nSmale\'s first problem


History:

formulation date | 1859  (158 years ago)\nformulator | Bernhard Riemann\nstatus | open


Associated equation:

Re(rho_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.\nConrey (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