Section: New Results

Numerical Evaluation of Elliptic Functions, Elliptic Integrals and Modular Forms

Participant : Fredrik Johansson.

In [33], F. Johansson describes algorithms to compute elliptic functions and their relatives (Jacobi theta functions, modular forms, elliptic integrals, and the arithmetic-geometric mean) numerically to arbitrary precision with rigorous error bounds for arbitrary complex variables. Implementations in ball arithmetic are available in the Arb library. This overview article discusses the standard algorithms from a concrete implementation point of view, and also presents some improvements.