Elliptic Curves pp 183-201 | Cite as

# Theta Functions

Chapter

## Abstract

Theta functions provide another source of elliptic functions as quotients of theta functions. They are defined for a lattice *L* of the form *L* _{τ} = **Z**τ + **Z** with **lm**(*τ*) > 0. This is no restriction, because every lattice *L* is equivalent to some *L* _{τ}. Since these functions *f*(*z*) are always periodic *f*(*z*) = *f*(*z* + 1), we will consider their expansions in terms of *q* _{ z } = *e* ^{2piz} where *f*(*z*) = *f**(*q* _{z}) and *f** is defined on **C*** = **C** — {0}. In §1 we consider various expansions in the variable *q* = *q* _{ z } of functions introduced in the previous chapter.

## Keywords

Meromorphic Function Elliptic Curve Elliptic Curf Elliptic Function Theta Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1987