Show the given function, Suppose that a1,...,ar and

Show the given function

Reference no: EM131350776

Suppose that a1,...,ar and b1,...,br are the zeros and poles, respectively, in the fundamental parallelogram of an elliptic function f. Show that

a₁ + ... + a_r - b₁ - ... - b_r =nw₁ + mw₂

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.]

Reference no: EM131350776

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