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21 Multidimensional Theta FunctionsComputation

§21.10 Methods of Computation

Contents

§21.10(i) General Riemann Theta Functions

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:

  • 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).

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

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