File:Zeta0.5 100 abs.svg

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DescriptionZeta0.5 100 abs.svg	$\|\zeta (\textstyle {\frac {1}{2}}+\mathrm {i} t)\|$ English: Riemann-Zeta-function absolute value on the critical line from 0 to 100. note that $\|\zeta (\textstyle {\frac {1}{2}}-\mathrm {i} t)\|=\|\zeta (\textstyle {\frac {1}{2}}+\mathrm {i} t)\|$
Date	December 2008
Source	Own work
Author	Geek3
Other versions	Zeta0.5 100.svg

Mathematical Function Plot
Description	Plot of the Riemann Zeta function
Equation	$y=\|\zeta (\textstyle {\frac {1}{2}}+\mathrm {i} x)\|$
Coordinate System	Cartesian
X Range	$[0,100]$
Y Range	$\mathbb {R}$
Accuracy	0.00001

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	22:14, 28 December 2008		680 × 720 (56 KB)	Geek3 (talk \| contribs)	{{Information \|Description=Absolute value of the Riemann zeta function \|Source=Own work \|Author=Geek3 \|Date= \|Permission= \|other_versions= }} <!--{{ImageUpload\|full}}-->

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Short title

Zeta0.5_100_abs.svg - absolute value of

    the Riemann-Zeta-function

on the critical line from 0 to 100

Image title

    Riemann-Zeta-function
    from Wikimedia Commons
    plot-range: real=1/2;  imaginary=[0 to 100]
    note that Abs(Zeta(1/2 - ix)) =  Abs(Zeta(1/2 + ix))

    plotted with several adapted cubic bezier-curves
    The plotcurve was calculated by some fancy code. The bezier-curve
    controlpoints are placed on tangents of the function-curve. They are
    furthermore positioned in a way to minimize the average quadratic distance
    between the bezier-curve and the function. This gives an accuracy, so that
    the deviation is in no point greater than 0.00001.

    symbols in "Computer Modern" (TeX) font embedded
    created with a plain text editor using GNU/Linux

    about: http://commons.wikimedia.org/wiki/Image:Zeta0.5_100_abs.svg
    source: http://commons.wikimedia.org/
    rights: GNU Free Documentation license,
            Creative Commons Attribution ShareAlike license

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Creative Commons Attribution-ShareAlike 2.0 Generic

GNU Free Documentation License, version 1.2 or later

Creative Commons Attribution-ShareAlike 1.0 Generic

Creative Commons Attribution-ShareAlike 2.5 Generic

Creative Commons Attribution-ShareAlike 3.0 Unported

source of file

original creation by uploader

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December 2008

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