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I tried to use Michael Trott's Mathematica Resource function RiemannSurfacePlot3D for plotting the Riemann surface of the Arg function without success. How can I plot this Riemann function with the Wolfram language?

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    $\begingroup$ Please show your code. $\endgroup$ Dec 26, 2023 at 22:36
  • $\begingroup$ As far as I can see the graph of arg z is plotted there, mathematica.stackexchange.com/a/114853/9469. Please have a look at the imaginary part of the logarithm function. Please notice $\mathrm{Log} z= \log|z|+i\mathrm{Arg} z$ $\endgroup$
    – yarchik
    Dec 28, 2023 at 3:57

1 Answer 1

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Please try this:

ComplexPlot3D[Arg[z], {z, -1 - I, 1 + I}]

UPDATE

Okay, understood. We cannot display infinitely many sheets, $\cdots,$ but we can display a few of them. Here are 21:

Plot3D[Table[ArcTan[x, y] + 2 \[Pi] k, {k, -10, 10}], {x, -1, 1}, {y, -1, 1}, 
       ColorFunction -> Function[{x, y, z}, Hue[21 z]]]

enter image description here

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  • $\begingroup$ Thanks, but this is a plot of Abs[Arg[z]] not a Riemann surface which has infinite sheets $\endgroup$
    – CharlesG
    Dec 27, 2023 at 9:47
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    $\begingroup$ Ok, thanks for so many sheets! :) $\endgroup$
    – CharlesG
    Dec 27, 2023 at 21:34

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