Dosiero:Discriminant real part.jpeg

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Modular discrimnant, real part, as function of nome. (600x600 pixels)

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[redaktu] Detailed description

This image shows the real part of the modular discriminant \Delta=g_2^3-27g_3^2=(2\pi)^{12}\eta^{24} 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 along the edge of the disk. Black areas indicate regions where the real part is zero or negative; blue/green areas where the value is small and positive, yellow/red where it is large and positive. 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 the above, g2=60 G4 and g3=140 G6 are Weierstrass elliptic functions invarients, whereas η is the Dedekind eta function.

See also Image:Gee_three_real.jpeg and Image:Gee_three_imag.jpeg for the real and imaginary parts of g3.

The imaginary part is quite similar. 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 14 February 2005 using custom software written entirely by Linas Vepstas.

[redaktu] Copyright status

Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.

Permeso estas donita kopii, distribui kaj/aŭ modifi tiun ĉi verkon sub la kondiĉoj de la GNU Free Documentation License, Versio 1.2 aŭ ia ajn alia versio eldonita de la Free Software Foundation; kun neniaj Senvariaj Sekcioj, neniaj Antaŭ-Kovrilaj Tekstoj, kaj neniaj Malantaŭ-Kovrilaj Tekstoj.
Kondiĉe de malgarantioj.

[redaktu] Relevant Links

  • Weierstrass elliptic functions
  • Eisenstein series
  • Q-series
date/time username edit summary
03:40, 18 May 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Discriminant_real_part.jpeg#Detailed_description" title="Image:Discriminant real part.jpeg">→</a>Detailed description -</span> fix several ommissions)
15:59, 15 February 2005 en:User:Linas (<span class="autocomment"><a href="/wiki/Image:Discriminant_real_part.jpeg#Detailed_description" title="Image:Discriminant real part.jpeg">→</a>Detailed description</span>)
04:50, 15 February 2005 en:User:Linas (fix formula)
04:22, 15 February 2005 en:User:Linas (fix forumula)
04:19, 15 February 2005 en:User:Linas
04:11, 15 February 2005 en:User:Linas (Modular discrimnant, real part, as function of nome.)

[redaktu] Historio de la dosiero

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  • (del) (cur) 04:11, 15 February 2005 . . en:User:Linas Linas ( en:User_talk:Linas Talk) . . 600x600 (67813 bytes) (Modular discrimnant, real part, as function of nome.)

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(nun)18:56, 18. Mar 2006Maksim-bot (Diskuto | kontribuoj)600×60066 KBLa bildo estas kopiita de wikipedia:en. La originala priskribo estas: Modular discrimnant, real part, as function of nome. (600x600 pixels) ===Detailed description=== This image shows the real part of the modular discr

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