Dosiero:J-inv-modulus.jpeg
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La bildo estas kopiita de wikipedia:en. La originala priskribo estas:
Klein's J-invariant, modulus portrait (600x600 pixels)
Enhavo |
[redaktu] Detailed description
This image shows the modulus | j | of the J-invariant as a function of the square of the nome q = exp(iπτ) on the unit disk |q| < 1. That is, πτ runs from 0 to 2π along the edge of the disk. Black indicates regions where the modulus is near zero, green where the modulus is about one, and red where the modulus is greater than ten. The color scale is logarithmic. Inside of every black region is a zero; note the zeros are cubic.
The small black dot on the far right, in the large red cardioid, is a numerical artifact.
The fractal self-similarity of this function is that of the modular group; note that this function is a modular form. Every modular function will have this general kind of self-similarity. In this sense, this particular image clearly illustrates the tesselation of the q-disk by the modular group.
- See also Image:J-inv-poincare.jpeg for this J-invariant on the Poincare disk.
- See also Image:J-inv-real.jpeg for the real part.
- See also Image:J-inv-phase.jpeg for the phase.
It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html
[redaktu] Source of Image
Created by Linas Vepstas User:Linas <linas@linas.org> on 21 May 2005 using custom software written entirely by Linas Vepstas.
[redaktu] Copyright status
Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas. Ŝablono:Gfdl
[redaktu] Relevant Links
- Weierstrass elliptic functions
- Eisenstein series
- Q-series
date/time | username | edit summary |
---|---|---|
04:43, 29 May 2005 | en:User:Linas | (<span class="autocomment"><a href="/wiki/Image:J-inv-modulus.jpeg#Detailed_description" title="Image:J-inv-modulus.jpeg">→</a>Detailed description -</span> tweaks, back-links) |
21:32, 21 May 2005 | en:User:Linas | (<span class="autocomment"><a href="/wiki/Image:J-inv-modulus.jpeg#Detailed_description" title="Image:J-inv-modulus.jpeg">→</a>Detailed description -</span> typo) |
21:31, 21 May 2005 | en:User:Linas | (<span class="autocomment"><a href="/wiki/Image:J-inv-modulus.jpeg#Detailed_description" title="Image:J-inv-modulus.jpeg">→</a>Detailed description -</span> corrections) |
21:27, 21 May 2005 | en:User:Linas | (add text, license) |
21:21, 21 May 2005 | en:User:Linas | (Klein's J-invariant, modulus portrait (600x600 pixels)) |
[redaktu] Historio de la dosiero
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- (del) (cur) 21:21, 21 May 2005 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 600x600 (36743 bytes) (Klein's J-invariant, modulus portrait (600x600 pixels))
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- (for) (nun) 14:58, 19. Mar 2006 . . Maksim-bot (Diskuto | kontribuoj) . . 600×600 (36 743 bitokoj) (La bildo estas kopiita de wikipedia:en. La originala priskribo estas: Klein's J-invariant, modulus portrait (600x600 pixels) ===Detailed description=== This image shows the modulus <math>|j|</math> of the J-invariant <math>j=g_2^3/\Delta</math> as)
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