On the fundamental units of some cubic orders generated by units

Jun Ho Lee, and Stéphane R. Louboutin. "On the fundamental units of some cubic orders generated by units." Acta Arithmetica 165.3 (2014): 283-299. <http://eudml.org/doc/279461>.

@article{JunHoLee2014,
abstract = {Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether \{ϵ,ϵ'\} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic polynomials are considered. We also improve upon and correct several previous results in the literature.},
author = {Jun Ho Lee, Stéphane R. Louboutin},
journal = {Acta Arithmetica},
keywords = {cubic orders; cubic units; system of fundamental units},
language = {eng},
number = {3},
pages = {283-299},
title = {On the fundamental units of some cubic orders generated by units},
url = {http://eudml.org/doc/279461},
volume = {165},
year = {2014},
}

TY - JOUR
AU - Jun Ho Lee
AU - Stéphane R. Louboutin
TI - On the fundamental units of some cubic orders generated by units
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 3
SP - 283
EP - 299
AB - Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic polynomials are considered. We also improve upon and correct several previous results in the literature.
LA - eng
KW - cubic orders; cubic units; system of fundamental units
UR - http://eudml.org/doc/279461
ER -