2. Suppose that a,..., ar and b,..., br. are the zeros and poles, respectively, in the...

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2. Suppose that a,..., ar and b,..., br. are the zeros and poles, respectively, in the fundamental parallelogram of an elliptic function f. Show that 3. Exercises a1ar - b - -br = nw1 +mw2 279 for some integers n and m. [Hint: If the boundary of the parallelogram contains no zeros or poles, simply inte- grate 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 2i. 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.] 2. Suppose that a,..., ar and b,..., br. are the zeros and poles, respectively, in the fundamental parallelogram of an elliptic function f. Show that 3. Exercises a1ar - b - -br = nw1 +mw2 279 for some integers n and m. [Hint: If the boundary of the parallelogram contains no zeros or poles, simply inte- grate 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 2i. 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.]