# order of an elliptic function

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

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 |