 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-2/13d/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Choose a fundamental parallelogram with no pole on its boundary. Opposite sides are translates traversed in opposite directions, so periodicity gives

\oint_{\partial P} f (z) d z = 0.

\sum_{j} Res (f; z_{j}) = 0.

A lone simple pole has a nonzero residue by definition of its order, so an elliptic function cannot have exactly one simple pole in a fundamental cell.

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