Let $\wp$ be the Weierstrass elliptic function. Is there a meromorphic function $f$ from $\mathbb{C}/L$ such that $f'(z) = \wp(z)$? Here $L$ is the usual lattice $(m\omega_1 + n\omega_2 | m,n \in \mathbb{Z})$.

As a hint I am given "What would the poles of $f$ look like?" but I have no idea how to think on this.

  • $\begingroup$ The poles of $\wp$ look like $1/z^2$, so the poles of $f$ would look like $1/z$. $\endgroup$ – mr_e_man May 7 at 20:37
  • 1
    $\begingroup$ Could you just integrate the series definition termwise? $$\wp(z)=\sum_{\omega\in L}\bigg(\frac{1}{(z-\omega)^2}-\frac{1}{\omega^2}\bigg)$$ $$f(z)=\sum_{\omega\in L}\bigg(\frac{-1}{z-\omega}-\frac{z}{\omega^2}\bigg)$$ $\endgroup$ – mr_e_man May 7 at 20:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.