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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Riemann hypothesis: Related Content

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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

Bohr–Landau theorem prime number theorem Riemann zeta function 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 amicable numbers Fermat’s last theorem perfect number

Key People

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

Bernhard Riemann

German mathematician

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Numbers and Mathematics