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Computing Riemann Theta Functions

Bernard Deconinck·Matthias Heil·Alexander Bobenko·Mark van Hoeij·Markus Schmies
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Abstract

The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision. This formula is used to construct a uniform approximation formula, again with arbitrary precision.

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Bernard Deconinck, Matthias Heil, Alexander Bobenko, Mark van Hoeij, Markus Schmies. 2002-07-03. Computing Riemann Theta Functions. https://arxiv.org/abs/nlin/0206009

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