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Pfaffian definitions of Weierstrass elliptic functions

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arxiv 1709.05224 v3 pith:6BYG4DB7 submitted 2017-09-15 math.NT math.LO

Gareth Jones , Harry Schmidt This is my paper · ORCID
classification math.NTmath.LO
keywords ellipticfunctionsgiveweierstrassdefinitionsexplicitpfaffianadditive
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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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  1. On the torsion values for sections of an elliptic scheme

    math.AG 2019-09 conditional novelty 7.0 of 10

    The canonical height of a section of an elliptic scheme over a curve equals the integral of the Betti form over the base, and this measure coincides with the dynamical equidistribution measure.

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