Computing Riemann Theta Functions
Exactly Solvable and Integrable Systems
2007-05-23 v2 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.nlin/0206009,
title = {Computing Riemann Theta Functions},
author = {Bernard Deconinck and Matthias Heil and Alexander Bobenko and Mark van Hoeij and Markus Schmies},
journal= {arXiv preprint arXiv:nlin/0206009},
year = {2007}
}
Comments
28 pages, 22 figures. Version with high resolution figures available from http://www.math.colostate.edu/~deconinc/papers.html. Some typos corrected in web addresses