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arXiv · 1709.05224

Pfaffian definitions of Weierstrass elliptic functions

Gareth Jones·Harry Schmidt
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Abstract

We give explicit definitions of the Weierstrass elliptic functions $\wp$ and $\zeta$ in terms of pfaffian functions, with complexity independent of the lattice involved. We also give such a definition for a modification of the Weierstrass function $\sigma$. As immediate applications, we give an explicit uniform zero estimate for $\wp$ and answer a question of Corvaja, Masser and Zannier on additive extensions of elliptic curves.

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Gareth Jones, Harry Schmidt. 2017-09-15. Pfaffian definitions of Weierstrass elliptic functions. https://arxiv.org/abs/1709.05224

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