Riemann hypothesis

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Other than the “trivial zeros” along the negative real axis, all the solutions to the Riemann zeta function must lie in the critical strip of complex numbers whose real part is between 0 and 1. The Riemann hypothesis is that all these nontrivial zeros actually lie on the critical line, or Re(S) = 12.

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Other than the “trivial zeros” along the negative real axis, all the solutions to the Riemann zeta function must lie in the critical strip of complex numbers whose real part is between 0 and 1. The Riemann hypothesis is that all these nontrivial zeros actually lie on the critical line, or Re(S) = 12.

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Topics

prime number theorem Riemann zeta function Bohr–Landau theorem number theory Millennium Problem P versus NP problem Poincaré conjecture Navier-Stokes equation Yang-Mills theory Hodge conjecture Birch and Swinnerton-Dyer conjecture twin prime conjecture perfect number Fermat’s last theorem Chinese remainder theorem

Key People

Bernhard Riemann, lithograph after a portrait, artist unknown, 1863.

Bernhard Riemann

German mathematician

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