Computing Riemann theta functions

Deconinck, Bernard; Heil, Matthias; Bobenko, Alexander; van Hoeij, Mark; Schmies, Marcus

doi:10.1090/S0025-5718-03-01609-0

Computing Riemann theta functions
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by Bernard Deconinck, Matthias Heil, Alexander Bobenko, Mark van Hoeij and Marcus Schmies PDF

Math. Comp. 73 (2004), 1417-1442 Request permission

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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