We know that every elliptic functions can be written as a rational function of $\wp$ and $\wp'$, where $\wp$ is the Weierstrass p function.. However, I am wondering how, given two arbitrary points $P$ and $Q$ on the fundamental parallelogram, we can build an elliptic function that has simple poles at $P$ and $Q$ using the function $\wp$. My professor was mentioning how we could use line integrals based on the $\wp$ function, but I couldn't keep up with his argument.
2026-03-25 15:43:44.1774453424
Given two points $P$ and $Q$ on a fundamental parallelogram, construct an elliptic function with simple poles at $P, Q$ by contour integral of $\wp$
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