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Elliptic Functions by W. F. Eberlein, J. V. Armitage

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3 General properties of elliptic functions

3.1 Apologia

The only unconventional thing about this chapter is its placement and we believe that Gauss, Abel, and Jacobi might even contest that. Historically, the general properties of elliptic functions (that is, doubly periodic functions meromorphic in the finite complex plane) were investigated after those remarkable objects were known to exist, but since the time of Weierstrass it has been conventional to discuss general properties before proving that examples existed. Since we have already constructed the Jacobian elliptic functions in Chapter 2, we can afford to return to what we believe to be the proper and historical order.

3.2 Period modules and lattices

We consider functions f(z) meromorphic ...

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