File:RiemannCriticalLine.svg

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Original file (SVG file, nominally 933 × 434 pixels, file size: 50 KB)

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Summary

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Description
English: Graph of real (red) and imaginary (blue) parts of the critical line Re(z)=1/2 of the Riemann zeta function.
Date
Source

Own work. Made with Mathematica using the following code:

Show[Plot[{Re[Zeta[1/2+I x]], Im[Zeta[1/2+I x]]}, {x,-30, 30},AxesLabel->{"x"} , PlotStyle->{Red, Blue}, Ticks->{Table[4x-28,{x,0,14}]}, ImageSize->{800,600}], Graphics[Text[Style[\[DoubleStruckCapitalR][\[Zeta][ I x + "1/2"]],14,Red ,Background ->White],{-22,2.6} ]], Graphics[Text[Style[\[GothicCapitalI][\[Zeta][ I x + "1/2"]],14,Blue ,Background ->White],{-14,2.6} ]]]
Author Slonzor
Permission
(Reusing this file)		 Public Domain
SVG development
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The SVG code is valid.
 
This plot was created with Matplotlib by Krishnavedala.
Source code
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Python code

Source code 
import mpmath
import numpy as np
from matplotlib import pyplot as plt
plt.rcParams['svg.fonttype'] = 'path'

x = np.linspace(-30, 30, 300)
y = [complex(1,1)]*len(x)
for p, xx in enumerate(x):
    t = mpmath.nstr(mpmath.mpc(0.5 + xx*1j))
    y[p] = mpmath.zeta(t)

fig = plt.figure(figsize=[13,6])
ax = fig.add_subplot(111)

ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
ax.spines['left'].set_smart_bounds(True)
ax.spines['bottom'].set_smart_bounds(True)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')

ax.text(-25,2.7, '$\\Re\\left[\\zeta\\left(\\frac{1}{2}+ix\\right)\\right]$', size='xx-large', color='red')
ax.text(-15,2.7, '$\\Im\\left[\\zeta\\left(\\frac{1}{2}+ix\\right)\\right]$', size='xx-large', color='blue')

ax.plot(x, [yy.real for yy in y], label='Real', color='red')
ax.plot(x, [yy.imag for yy in y], label='Imag', color='blue')
# ax.legend(loc=(.6,.8))
ax.minorticks_on()
ax.grid(b=True, which='major', ls='-', lw=1.5)
ax.grid(b=True, which='minor', ls='--', lw=.5)
fig.savefig('RiemannCriticalLine.svg', bbox_inches='tight')

Licensing

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Public domain 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.

File history

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Date/TimeThumbnailDimensionsUserComment
current20:01, 23 August 2017Thumbnail for version as of 20:01, 23 August 2017933 × 434 (50 KB)Krishnavedala (talk | contribs)much reduced vector version
22:28, 24 September 2009Thumbnail for version as of 22:28, 24 September 2009800 × 600 (122 KB)Geek3 (talk | contribs)linewidth=1px
19:33, 20 November 2008Thumbnail for version as of 19:33, 20 November 2008800 × 600 (122 KB)Slonzor (talk | contribs)Man i've messed this up a lot of times.
19:27, 20 November 2008Thumbnail for version as of 19:27, 20 November 2008800 × 600 (3.36 MB)Slonzor (talk | contribs)
19:23, 20 November 2008Thumbnail for version as of 19:23, 20 November 2008800 × 600 (3.36 MB)Slonzor (talk | contribs)
19:18, 20 November 2008Thumbnail for version as of 19:18, 20 November 2008800 × 600 (3.36 MB)Slonzor (talk | contribs)
19:13, 20 November 2008Thumbnail for version as of 19:13, 20 November 2008800 × 600 (79 KB)Slonzor (talk | contribs){{Information |Description={{en|1=Graph of real (red) and imaginary (blue) parts of the critical line Re(z)=1/2 of the Riemann zeta function.}} |Source=Own work. Made with Mathematica using the following code: <code><nowiki>Show[Plot[{Re[Zeta[1/2+I x]],

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