Pfaffian definitions of Weierstrass elliptic functionsCitation formats

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Pfaffian definitions of Weierstrass elliptic functions. / Jones, Gareth; Schmidt, Harry.

In: Mathematische Annalen, Vol. 2020, No. 0, 06.02.2020, p. 0.

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Jones, G & Schmidt, H 2020, 'Pfaffian definitions of Weierstrass elliptic functions', Mathematische Annalen, vol. 2020, no. 0, pp. 0. https://doi.org/10.1007/s00208-019-01948-8

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Jones, Gareth ; Schmidt, Harry. / Pfaffian definitions of Weierstrass elliptic functions. In: Mathematische Annalen. 2020 ; Vol. 2020, No. 0. pp. 0.

Bibtex

@article{75f630e098624776aced1415776e45d6,
title = "Pfaffian definitions of Weierstrass elliptic functions",
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. 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.",
author = "Gareth Jones and Harry Schmidt",
note = "Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = feb,
day = "6",
doi = "10.1007/s00208-019-01948-8",
language = "English",
volume = "2020",
pages = "0",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer Nature",
number = "0",

}

RIS

TY - JOUR

T1 - Pfaffian definitions of Weierstrass elliptic functions

AU - Jones, Gareth

AU - Schmidt, Harry

N1 - Publisher Copyright: © 2020, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/2/6

Y1 - 2020/2/6

N2 - 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.

AB - 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.

U2 - 10.1007/s00208-019-01948-8

DO - 10.1007/s00208-019-01948-8

M3 - Article

VL - 2020

SP - 0

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 0

ER -