= Elliptic divisor-sum identity
{title2=$\sum_j r_jz_j-\sum_l m_lp_l\in\Lambda$}
For a nonzero <elliptic function>, the weighted sum of its zero positions minus its pole positions belongs to the <period lattice>. Integrating $zf^{\prime}/f$ around a <fundamental parallelogram> proves this: translating opposite edges gives a lattice-linear combination of integrals of $f^{\prime}/f$, each an integer multiple of $2\pi i$. The unweighted integral proves that the zero and pole multiplicities have equal total.
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