order of an elliptic function

The order of an elliptic functionMathworldPlanetmath is the number of poles of the functionMathworldPlanetmath contained within a fundamental period parallelogram, counted with multiplicity. Sometimes the term “degree” is also used — this usage agrees with the theory of Riemann surfacesDlmfPlanetmath.

This order is always a finite number; this follows from the fact that a meromorphic function can only have a finite number of poles in a compact region (such as the closure of a period parallelogram). As it turns out, the order can be any integer greater than 1.

Title order of an elliptic function
Canonical name OrderOfAnEllipticFunction
Date of creation 2013-03-22 15:44:35
Last modified on 2013-03-22 15:44:35
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 8
Author rspuzio (6075)
Entry type Definition
Classification msc 33E05