A few months ago I got my copy of Mathematica 8. It wasn’t until a few days ago that I learned how to plot the Riemann zeta function in the complex plane. I did not figure this out myself, instead I searched Google and found Jeffrey Stopple’s home page here with some of his Mathematica code:

`Show[Graphics[RasterArray[Table[Hue[Mod[3 Pi/2 + Arg[Zeta[sigma + I t]], 2 Pi]/(2 Pi)], {t, -30, 30, .1}, {sigma, -30, 30, .1}]]], AspectRatio -> Automatic]`

Wikipedia has perhaps the best plot. It is however possible to plot the argument of the Riemann zeta function in Wolfram Alpha with this short command:

`ContourPlot[Arg[Zeta[s + I t]], {s, -30, 30}, {t, -30, 30}]`

Link to the contourplot in Wolfram Alpha.

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