Pauli, Sebastian (2001) *Efficient enumeration of extensions of local fields with bounded discriminant.* PhD thesis, Concordia University.

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## Abstract

Let k be a p -adic field. It is well-known that k has only finitely many extensions of a given finite degree. Krasner [1966] gives formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions K / k of a given degree and discriminant. We also present canonical sets of generating polynomials of extensions of degree p m . Some methods from the proof of the number of extensions of a given degree and discriminant can also be used for the determination of a bound that gives a considerably improved estimate of the complexity of polynomial factorization over local fields. We use this bound in an efficient new algorithm for factoring a polynomial Z over a local field k . For every irreducible factor [varphi]( x ) of Z ( x ) our algorithm return an integral basis for k [ x ]/[varphi]( x ) k [ x ] over k .

Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
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Item Type: | Thesis (PhD) |

Authors: | Pauli, Sebastian |

Pagination: | viii, 96 leaves ; 29 cm. |

Institution: | Concordia University |

Degree Name: | Theses (Ph.D.) |

Program: | Mathematics and Statistics |

Date: | 2001 |

Thesis Supervisor(s): | Ford, David |

ID Code: | 1533 |

Deposited By: | Concordia University Libraries |

Deposited On: | 27 Aug 2009 13:20 |

Last Modified: | 08 Dec 2010 10:21 |

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