Abstract
Let ω 1, ω 2 be two complex numbers which are linearly independent over the reals. Let L be the lattice spanned by ω 1, ω 2. That is,
An elliptic function (relative to the lattice L) is a meromorphic function f on \(\mathbb{C}\) (thus an analytic map \(f: \mathbb{C} \rightarrow \mathbb{C}\mathbb{P}_{1}\)) which satisfies
for all ω ∈ L and \(z \in \mathbb{C}\).
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Bibliography
M. Waldschmidt, Transcendance et exponentielles en plusieurs variables. Invent. Math. 63(1), 97–127 (1981)
A. Weil, Elliptic Functions According to Eisenstein and Kronecker (Springer, Berlin, 1999)
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Murty, M.R., Rath, P. (2014). Elliptic Functions. In: Transcendental Numbers. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0832-5_10
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DOI: https://doi.org/10.1007/978-1-4939-0832-5_10
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