Développements périodiques de familles paramétrées de nombres algébriquues : application à la recherche d'unité

Abstract : The main purpose of this work is the study of parametried families and the surch of fundamental units of these fields. We give the Voronoï algorithm expansion of two families of complex cubic fields, introduced by C. Levesque and G. Rhin and so we obtain a fundamental unit of these fields. We compare this expansion with Jacobi-Perron algorithm expansion and notice that they are closely connected for these two families. Then we proceed to several generalizations. First, we generalize these families to parametrized families of fields with degree higher than three. We study an expansion by the Jacobi-Perron algorithm and so we obtain an unit of these fields. Next, we give a generalization of Voronoï algorithm, which consists in the search of minimal points. We give a more general definition of minimal points and propose a new method to compute these points. Then, we conjecture sevral expansions of quartic numbers fields of unit rank 2. In the last part of this work, we describe an algorithm which allows us to compute the Jacobi-Perron algorithm (and particularly the continued fraction algorithm) expansion of algebraic numbers, using only integers
Document type :
Theses
Complete list of metadatas

Cited literature [28 references]  Display  Hide  Download

https://hal.univ-lorraine.fr/tel-01777079
Contributor : Administrateur Du Ccsd <>
Submitted on : Tuesday, April 24, 2018 - 4:10:30 PM
Last modification on : Thursday, April 26, 2018 - 1:28:31 AM
Long-term archiving on : Wednesday, September 19, 2018 - 3:26:22 PM

File

Adam.Brigitte.SMZ9525.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01777079, version 1

Collections

Citation

Brigitte Adam. Développements périodiques de familles paramétrées de nombres algébriquues : application à la recherche d'unité. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1995. Français. ⟨NNT : 1995METZ025S⟩. ⟨tel-01777079⟩

Share

Metrics

Record views

21

Files downloads

19