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Almost as a follow on from this old question, I am having similar problems again, with slight difference, that if the values are small enough, a completely blank plot is produced.

ξ[z_] := ((z - 1) Gamma[z/2 + 1] Zeta[z])/Sqrt[π^z]

ContourPlot[{Im[ξ[σ + b I]], Re[ξ[σ + b I]]}, {σ, -2, 3}, {b, 100, 120},
            PlotPoints -> 500]

enter image description here

Even with PlotPoints->500 there are still breaks in the plot. I know I am dealing with very small numbers here, but is there anything I can do to create a clean plot?

The plot above is not too bad, but I would really like to look at plots for values of {b,7000,7010} - but it just produces a blank plot above 1000. Is there anything I can to to avoid this?

Update

Have tried Exclusions->None but creates a plot that is just wrong!

enter image description here

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1  
try Exclusions->None !Mathematica graphics –  Nasser Mar 4 at 10:04
    
Have tried that - what's with the grid? Is that part of the plot? Also, no luck on the higher values - still blank. –  martin Mar 4 at 10:15

1 Answer 1

up vote 5 down vote accepted

I'm not sure this is on the right track, if so OP just comment and I'll delete. I've found that plotting can get finicky with very large/very small values, and have in the past "helped" by lifting values into a more "reasonable" range. E.G. (I picked a scaling for a "middle" value of the plot range):

ξ[z_] := ((z - 1) Gamma[z/2 + 1] Zeta[z])/Sqrt[π^z]
ContourPlot[{Im[ξ[σ + b I]]*10^2380,  Re[ξ[σ + b I]]*10^2380}, 
             {σ, -2, 3}, {b, 7000, 7010}, PlotPoints -> 100, MaxRecursion -> 2, 
             PerformanceGoal -> "Speed", Contours -> 20, PlotRange -> Automatic]

enter image description here

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@ rasher, thanks for the advice - a simple solution that at least lets me see what's going on up there! –  martin Mar 4 at 12:01
1  
@martin: Glad it seems it is useful, appreciate the accept, but don't hesitate to reverse if a better answer comes along: this is what I've used, since I've not come across a better way (yet). –  rasher Mar 4 at 12:05
    
@rasher we seem to be in-sync tonight...I originally plotted using the scaling...a bit slow (played with log)+1...nice looking plot will delete mine –  ubpdqn Mar 4 at 12:30
    
@ubpdqn: ;-} I hope MMA 10 has improved this (and similar problems with ticks for very wide ranges). –  rasher Mar 4 at 21:19

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