Pfaffian definitions of Weierstrass elliptic functions

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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. Our work has immediate applications to Diophantine geometry and we answer a question of Corvaja, Masser and Zannier on additive extensions of elliptic curves. We also point out further applications, also in connection with Pila–Wilkie type counting problems.

Bibliographical metadata

Original languageEnglish
Pages (from-to)0
JournalMathematische Annalen
Issue number0
Early online date6 Feb 2020
Publication statusPublished - 6 Feb 2020

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