Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm trying to prove that every elliptic function of order $2$ has the form


I've got the following so far. Let $f$ be an elliptic function of order 2. Then $f$ has $2$ poles and $2$ zeroes inside the fundamental parallelogram $P$ counting with multiplicity. Choose $z_0$ s.t. $f(z_0)$ is a pole. Now $f(z)=\wp(z-z_0)$ at $z=z_0$. But now I don't really know what to do, because the multiplicity of my pole of $\wp$ doesn't necessarily match that of $f$ does it? Could someone clarify this for me, and give me a hint on how to proceed?

Many thanks!

share|cite|improve this question
Don't worry - have worked it out now! – Edward Hughes May 31 '12 at 12:56
Could you outline your solution please, so that whoever in the future gets here doesn't have to ask again? Thanks! – Gregor Bruns May 31 '12 at 15:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.