File:Riemann critical line.png

Nonfiction: Riemann hypothesis: The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011.

In the News

Fiction cross-reference

Nonfiction cross-reference

• Bernhard Riemann (nonfiction)
• Mathematics (nonfiction)
• Riemann hypothesis (nonfiction)

External links:

• Riemann hypothesis @ Wikipedia

Attribution:

By Slonzor - Own work. Made with Mathematica using the following code: Show[Plot[{Re[Zeta[1/2+I x]], Im[Zeta[1/2+I x]]}, {x,-30, 30},AxesLabel->{"x"} , PlotStyle->{Red, Blue}, Ticks->{Table[4x-28,{x,0,14}]}, ImageSize->{800,600}], Graphics[Text[Style[\[DoubleStruckCapitalR][\[Zeta][ I x + "1/2"]],14,Red ,Background ->White],{-22,2.6} ]], Graphics[Text[Style[\[GothicCapitalI][\[Zeta][ I x + "1/2"]],14,Blue ,Background ->White],{-14,2.6} ]]], Public Domain, https://commons.wikimedia.org/w/index.php?curid=5240444