Groupe des unités pour des extensions diédrales complexes de degré 10 sur Q

Omar Kihel

Journal de théorie des nombres de Bordeaux (2001)

  • Volume: 13, Issue: 2, page 469-482
  • ISSN: 1246-7405

Abstract

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The purpose of this paper is to show that any set of four roots of the quintic polynomials exhibited by H. Darmon forms under certain conditions a fundamental system of units for the corresponding dihedral fields.

How to cite

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Kihel, Omar. "Groupe des unités pour des extensions diédrales complexes de degré $10$ sur $Q$." Journal de théorie des nombres de Bordeaux 13.2 (2001): 469-482. <http://eudml.org/doc/248703>.

@article{Kihel2001,
abstract = {Le but de cet article est de montrer qu’un ensemble quelconque de quatre racines des polynômes quintiques $p(x)$ exhibés par $H$. Darmon forme sous certaines conditions un système fondamental d’unités de la fermeture normale du corps $\mathbf \{Q\} (\theta )$ où $p (\theta )= 0$.},
author = {Kihel, Omar},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {dihedral Galois group; fundamental system of units; Galois extension},
language = {fre},
number = {2},
pages = {469-482},
publisher = {Université Bordeaux I},
title = {Groupe des unités pour des extensions diédrales complexes de degré $10$ sur $Q$},
url = {http://eudml.org/doc/248703},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Kihel, Omar
TI - Groupe des unités pour des extensions diédrales complexes de degré $10$ sur $Q$
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 2
SP - 469
EP - 482
AB - Le but de cet article est de montrer qu’un ensemble quelconque de quatre racines des polynômes quintiques $p(x)$ exhibés par $H$. Darmon forme sous certaines conditions un système fondamental d’unités de la fermeture normale du corps $\mathbf {Q} (\theta )$ où $p (\theta )= 0$.
LA - fre
KW - dihedral Galois group; fundamental system of units; Galois extension
UR - http://eudml.org/doc/248703
ER -

References

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  2. [2] K.K. Billevi, Sur les unités d'un corps algébrique de degré 3 ou 4. Mat. Sbornik N. S.40 (1956) (en russe). 
  3. [3] A. Brumer, On the group of units of an absolutely cyclic number field of prime degree. J. Math. Soc. Japan21 (1969), 357-358. Zbl0188.35301MR244193
  4. [4] T.W. Cusick, Lower bounds for regulators. Lecture Notes in Math.1068, 63-73, Springer, Berlin, 1984. Zbl0549.12003MR756083
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