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DedekindEta

  • DedekindEta[] gives the Dedekind eta modular elliptic function .
  • Mathematical function (see Section A.3.10).
  • DedekindEta is defined only in the upper half of the complex plane. It is not defined for real .
  • The argument is the ratio of Weierstrass half-periods .
  • DedekindEta satisfies where is the discriminant, given in terms of Weierstrass invariants by .
  • See Section 3.2.11 for a discussion of argument conventions for elliptic functions.
  • See the Mathematica book: Section 3.2.11.
  • See also: ModularLambda, KleinInvariantJ, EllipticTheta, PartitionsP.

    Further Examples

    The Dedekind eta function is defined by , for in the complex upper half-plane. If is regarded as the ratio of half-periods of an elliptic curve and are the corresponding Weierstrass coefficients, then .

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    Under fractional linear transformations of the complex plane with integer coefficients, the Dedekind eta function transforms in simple ways. The most obvious example of such a transformation (apart from the identity) is ; in this case .

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