Submission date: 15 September 2017

Abstract:

We give explicit definitions of the Weierstrass elliptic functions ℘ and ζ 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 σ. As immediate applications, we give an explicit uniform zero estimate for ℘ and answer a question of Corvaja, Masser and Zannier on additive extensions of elliptic curves.

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Full text arXiv 1709.05224: pdf, ps.