examples of elliptic functions
Let be a lattice generated by . Let denote .
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1.
The Weierstrass -function is defined by the series
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2.
The derivative of the Weierstrass -function is also an elliptic function
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3.
The Eisenstein series of weight for is the series
The Eisenstein series of weight and are of special relevance in the theory of elliptic curves. In particular, the quantities and are usually defined as follows:
Remark: The elliptic functions , and are related by the following important equation:
In particular, the previous equation provides an isomorphism between and the elliptic curve given by:
Title | examples of elliptic functions |
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Canonical name | ExamplesOfEllipticFunctions |
Date of creation | 2013-03-22 13:54:04 |
Last modified on | 2013-03-22 13:54:04 |
Owner | alozano (2414) |
Last modified by | alozano (2414) |
Numerical id | 7 |
Author | alozano (2414) |
Entry type | Example |
Classification | msc 33E05 |
Related topic | EllipticFunction |
Related topic | WeierstrassWpFunction |
Defines | Eisenstein series |