Meromorphic Function is Elliptic iff Doubly Periodic
Jump to navigation
Jump to search
This theorem requires a proof..
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
Contents
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
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
Historical Note
Meromorphic Function is Elliptic iff Doubly Periodic was discovered by Niels Henrik Abel during his exploration of elliptic functions.
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($1815$ – $1897$)
