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21 Multidimensional Theta FunctionsComputation

§21.10 Methods of Computation

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Permalink:
http://dlmf.nist.gov/21.10
See also:
Annotations for Ch.21
Contents
  1. §21.10(i) General Riemann Theta Functions
  2. §21.10(ii) Riemann Theta Functions Associated with a Riemann Surface

§21.10(i) General Riemann Theta Functions

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Referenced by:
§21.2(i), §21.2(i), Erratum (V1.0.5) for Subsection 21.10(i)
Permalink:
http://dlmf.nist.gov/21.10.i
Modification (effective with 1.0.5):
The entire original content of this subsection has been replaced by a reference.
See also:
Annotations for §21.10 and Ch.21

See Deconinck et al. (2004).

§21.10(ii) Riemann Theta Functions Associated with a Riemann Surface

In addition to evaluating the Fourier series, the main problem here is to compute a Riemann matrix originating from a Riemann surface. Various approaches are considered in the following references:

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    Belokolos et al. (1994, Chapter 5) and references therein. Here the Riemann surface is represented by the action of a Schottky group on a region of the complex plane. The same representation is used in Gianni et al. (1998).

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    Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.

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    Deconinck and van Hoeij (2001). Here a plane algebraic curve representation of the Riemann surface is used.

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