modular discriminant
Definition 1.
Let be a lattice.
-
1.
Let . The Dedekind eta function is defined to be
The Dedekind eta function should not be confused with the Weierstrass eta function, .
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2.
The -invariant, as a function of lattices, is defined to be:
where and are certain multiples of the Eisenstein series of weight and (see http://planetmath.org/encyclopedia/ExamplesOfEllipticFunctions.htmlthis entry).
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3.
The function (delta function or modular discriminant) is defined to be
Let be the lattice generated by . The function for has a product expansion
Title | modular discriminant |
Canonical name | ModularDiscriminant |
Date of creation | 2013-03-22 13:54:09 |
Last modified on | 2013-03-22 13:54:09 |
Owner | alozano (2414) |
Last modified by | alozano (2414) |
Numerical id | 6 |
Author | alozano (2414) |
Entry type | Definition |
Classification | msc 33E05 |
Synonym | delta function |
Related topic | EllipticFunction |
Related topic | JInvariant |
Related topic | WeierstrassSigmaFunction |
Related topic | Discriminant |
Related topic | DiscriminantOfANumberField |
Related topic | RamanujanTauFunction |
Defines | modular discriminant |
Defines | Dedekind eta function |