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| Keywords: PlotDiscriminantsOfComplexCubicFields.svg validSVG Created with Gnuplot en Plot of the number of complex cubic fields of bounded discriminant up to 10<sup>6</sup> and the asymptotic distribution Black line is the first order term of the asymptotic green line includes the second order term and blue crosses are the exact counts Data by Michel Olivier available at http //pari math u-bordeaux fr/pub/pari/packages/nftables/ Asymptotics from Bhargava “Shankar “Tsimerman On the Davenport “Heilbronn theorem and second order terms http //arxiv org/abs/1005 0672 arXiv 1005 0672 own RobHar 2010-06-06 Data file This image was created using gnuplot 4 2 4 with the following command file It was subsequently edited with Inkscape and a text editor to fix display problems wikipedia has set terminal svg enhanced fname Helvetica fsize 20 set output cubiccomplex svg Axes set size square make the graph square set logscale loglog plot set xrange 100 1000000 adjust axis range set yrange 1 200000 set xlabel Bound on Discriminant set ylabel Complex Cubic Fields set xlabel 0 0 0 5 adjust positioning of axis label set ylabel -2 1 0 0 tics set format 10 m L adjust format of tic labels set xtics offset 1 0 0 45 nomirror adjust placement of tic labels and nomirror tics set ytics offset 3 0 0 0 nomirror set mxtics 10 set number of minor tics set mytics 10 set grid xtics ytics lt rgb gray lw 1 set grid set style line 1 lt 3 pt 1 ps 0 9 set marker style to blue cross adjust size set style line 2 lt -1 lw 1 set marker style to black line set style line 3 lt 2 lw 1 set marker style to green thick line f x 0 207976843145176 x - 0 255798375633611 x 0 83333333333333333 g x 0 207976843145176 x plot cubiccomplexdata index 0 using 1 2 notitle with points linestyle 1 \ f x notitle with lines linestyle 3 \ g x notitle with lines linestyle 2 Number theory SVG diagrams Images with Gnuplot source code | ||||
