Solution
= Solution
Fix $w\in\mathbb C$ and apply the stated clockwise argument principle to $h=f-w$. Its logarithmic <derivative> is periodic, so the <integrals> over opposite sides of a fundamental cell cancel. Hence $P-Z=0$. The poles of $f-w$ are precisely the poles of $f$, with unchanged multiplicities, while its zeros are the solutions of $f(z)=w$. Thus the <value multiplicity of an elliptic function> is the same fixed pole count for every finite $w$, counting multiplicity.