# $f'(z) = \wp(z)$, Weierstrass $\wp$ function

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.

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