English: Plot of the number of complex cubic fields of bounded discriminant up to 106, 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 [1]. Asymptotics from Bhargava–Shankar–Tsimerman, "On the Davenport–Heilbronn theorem and second order terms", arXiv:1005.0672.
setterminalsvgenhancedfname"Helvetica"fsize20setoutput"cubiccomplex.svg"#Axessetsizesquare#make the graph squaresetlogscale#loglog plotsetxrange[100:1000000]#adjust axis rangesetyrange[1:200000]setxlabel"Bound on Discriminant"setylabel"Complex Cubic Fields"setxlabel0.0,0.5#adjust positioning of axis labelsetylabel-2.1,0.0#ticssetformat"@{10}&{m}^{%L}"#adjust format of tic labelssetxticsoffset1.0,0.45nomirror#adjust placement of tic labels, and nomirror ticssetyticsoffset3.0,0.0nomirrorsetmxtics10#set number of minor ticssetmytics10setgridxticsyticsltrgb"gray"lw1#set gridsetstyleline1lt3pt1ps0.9#set marker style to blue cross, adjust sizesetstyleline2lt-1lw1#set marker style to black linesetstyleline3lt2lw1#set marker style to green thick linef(x)=0.207976843145176*x-0.255798375633611*(x**(0.83333333333333333))g(x)=0.207976843145176*xplot"cubiccomplexdata"index0using1:2notitlewithpointslinestyle1,\
f(x)notitlewithlineslinestyle3,\
g(x)notitlewithlineslinestyle2
Licensing
Public domainPublic domainfalsefalse
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Captions
Add a one-line explanation of what this file represents
((Information |Description=((en|1=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, an
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):