Elliptic Functions

M. Ram Murty and Purusottam Rath
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M. Ram Murty: Queen’s University, Department of Mathematics and Statistics
Purusottam Rath: Chennai Mathematical Institute

Chapter Chapter 10 in Transcendental Numbers, 2014, pp 39-47 from Springer

Abstract: 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, L = { m ω 1 + n ω 2 : m , n ∈ ℤ } . $$\displaystyle{L =\{ m\omega _{1} + n\omega _{2}:\, m,n \in \mathbb{Z}\}.}$$ An elliptic function (relative to the lattice L) is a meromorphic function f on ℂ $$\mathbb{C}$$ (thus an analytic map f : ℂ → ℂ ℙ 1 $$f: \mathbb{C} \rightarrow \mathbb{C}\mathbb{P}_{1}$$ ) which satisfies f ( z + ω ) = f ( z ) $$\displaystyle{f(z+\omega ) = f(z)}$$ for all ω ∈ L and z ∈ ℂ $$z \in \mathbb{C}$$ .

Keywords: Elliptic Functions; Meromorphic Function; Weierstrass; Fundamental Domain; Entire Function (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4939-0832-5_10

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