|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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