Pfaffian definitions of Weierstrass elliptic functions

2017/09/15 by Jones, Gareth, Schmidt, Harry · 1 citation
#FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1709.05224

Abstract

We give explicit definitions of the Weierstrass elliptic functions \wp 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 \wp and answer a question of Corvaja, Masser and Zannier on additive extensions of elliptic curves.

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• Singular intersections in families of abelian varieties

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