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Sfb288 logo Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 560


Computing Riemann Theta Functions

B. Deconinck, M. Heil, A.I. Bobenko, M. van Hoeij, M. Schmies

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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