Abstract

The trigonometric functions are the basic functions that are periodic with respect to a translation of the plane \(\mathbb {C}\). An important class of complex functions is doubly periodic: periodic with respect to two sets of translations. This chapter presents the general theory of such functions, and Jacobi’s construction via theta functions. The following two chapters, which are independent of each other, present constructions due to Jacobi and to Weierstrass, respectively.

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