Image:Zeta polar.svg

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Zeta_polar.svg‎ (11KB, MIME type: image/svg+xml)

This image shows a polar graph of the Riemann zeta function along the critical line. That is, it is a graph of $\Re\zeta(it+1/2)$ versus $\Im\zeta(it+1/2)$ for real values of t running from 0 to 34. The first five zeros in the critical strip are clearly visible as the place where the spirals pass through the origin.

[edit] Data file

This image was created using gnuplot, from original data, using the following command file:

set term svg
set out 'zeta-imag.svg'
# set term png
# set out 'zeta-imag.png'
#
set data style lines
set key right
set xzeroaxis linetype -1 linewidth 2
set yzeroaxis linetype -1 linewidth 2
set xtics axis
set ytics axis
#
# set bmargin 2
# set lmargin 5
#
unset border
# set border 2
#
set title "Polar graph of Riemann zeta(1/2+it)"
set xlabel "Re zeta(it+1/2)"  0, 1
set ylabel "Im zeta(it+1/2)" 1, 8
plot "zeta-imag.dat" using 2:3 title "" with lines linewidth 2

[edit] Provenance

Original artwork created by Linas Vepstas <linas@linas.org> User:Linas 19 February 2006

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
Subject to disclaimers.

File history

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(del) (cur) 23:25, 19 February 2006 . . Linas (Talk | contribs) . . 600×480 (10,997 bytes) (Original artwork created by Linas Vepstas <linas@linas.org> User:Linas 19 February 2006)