# # Riemann zeta fuction # # Check support if (!strstrt(GPVAL_COMPILE_OPTIONS, "+COMPLEX_FUNC")) { print "This copy of gnuplot does not provide zeta(s)" exit # return to caller } save_encoding = GPVAL_ENCODING set encoding utf8 set title "Real and imaginary parts of ζ(s) along the critical line real(s) = 1/2" set grid x y set xzeroaxis set sample 999 set key reverse left set xrange [5:50] set yrange [-3:4] plot real(zeta( 0.5 + I*x )) lt 4 lw 3 title "real( ζ(½ + ix) )", \ imag(zeta( 0.5 + I*x )) lt 6 lw 3 title "imag( ζ(½ + ix) )" |
set title "{/Times=16 Riemann zeta function} {/Times:Italic=16 ζ(s) = {∑@_{/*0.5 {k=1}}^{/*.5 ∞}} {/:Italic=12 k^{ -s}}" set samp 201 set iso 201 set pm3d depth base noborder set pm3d interp 2,2 set pm3d lighting specular 0.1 set xyplane 0 unset colorbox set key left set border 895 set grid x y z vertical set xlabel "Real(s)" offset -1,0 right set ylabel "Imag(s)" set xrange [-9 : 9] set yrange [-9 : 9] set zrange [0 : 4] set palette defined (0 "dark-blue", 1 "white") set zrange [-1.1 : 2.2] splot real( zeta(x + I*y) ) with pm3d title "real(ζ(s))" |
set palette defined (0 "dark-red", 1 "white") set zrange [-0.55 : 0.55] splot imag( zeta(x + I*y) ) with pm3d title "imag(ζ(s))" |
set zrange [*:*] unset grid set view map set key right opaque box samplen 0 set colorbox set cblabel "Phase Angle" set cblabel offset -1, 0, 0 rotate set cbrange [ -3.14159 : 3.14159 ] noreverse writeback set cbtics ("-π" -pi, "+π" pi) set pm3d interp 1,1 nolighting corners2color c1 set palette color model HSV defined ( 0 0 1 1, 1 1 1 1 ) splot arg( zeta(x + I*y) ) with pm3d title "arg(ζ(s))" |
unset colorbox set palette cubehelix negative set pm3d lighting specular 0.1 set yrange [-10:50] set xrange [-3:3] set zrange [0:4] set view 57, 100, 1.2, 0.5 set key nobox noopaque bottom left at screen 0.0, 0.6 set xlabel offset -3 splot 1./abs( zeta(x + I*y) ) with pm3d title "|ζ(s)|^{-1}" |
set encoding save_encoding |