Computing Riemann Theta Functions

Details Computing Riemann Theta Functions Computing Riemann Theta Functions

2002-06-10

arxiv.org/abs/nlin/0206009v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

28 pages, 22 figures. Version with high resolution figures available from http://www.math.colostate.edu/~deconinc/papers.html.

Scientific paper

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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