Not sure if this has been asked before. I understand the proof that the sum of the residues of an elliptic function is zero. However I fail to see that an elliptic function of order one cannot have an irreducible pole of residue zero. I don't know if I'm missing something simple or not. I can't seem to find the answer anywhere.
2026-03-09 19:22:42.1773084162
Why do the simplest elliptic functions need to have order $2$?
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