# Meromorphic Function is Elliptic iff Doubly Periodic

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## Theorem

Let $f: \C \to \C$ be a meromorphic function.

Then $\map f z$ is an elliptic function if and only if it is also doubly periodic.

## Proof

## Historical Note

Meromorphic Function is Elliptic iff Doubly Periodic was discovered by Niels Henrik Abelâ€Ž during his exploration of elliptic functions.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$)