Suppose that a1,…,ar and b1,…,br are the zeros and poles, respectively, in the fundamental parallelogram of an elliptic function f. Show that
for some integers n and m.
[Hint: If the boundary of the parallelogram contains no zeros or poles, simply integrate zf’ (z)/f(z) over that boundary, and observe that the integral of f’ (z)/f(z) over a side is an integer multiple of 2πi. If there are zeros or poles on the side of the parallelogram, translate it by a small amount to reduce the problem to the first case.]
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