Abstract

Let ℘ be the Weierstrass function associated with an arbitrary lattice in the complex plane. We describe a fast iterative method (based on the duplication property of ℘) which allows us to compute ℘(z) for an arbitrary complex number z. We also describe an iterative method for computing the values of periods associated with any pair of complex Weierstrass invariants g2 and g3: the last method relies upon the arithmetic-geometric mean property of elliptic integrals.

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