Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 13D / a

An elliptic function is a meromorphic $f:\mathbb{C}\to \hat{\mathbb{C}}$ with two real-linearly independent periods ${\omega }_1,{\omega }_2$. A fundamental cell may be taken as the half-open parallelogramwith $z_0$ chosen so that its boundary contains no zero or pole under discussion. The argument principle and cancellation on opposite sides show that a nonconstant elliptic function has the same number of zeros and poles in a cell, counting multiplicity.