Fundamental units for orders of unit rank 1 and generated by a unit

@article{StéphaneR2016,
abstract = {Let ε be an algebraic unit for which the rank of the group of units of the order ℤ[ε] is equal to 1. Assume that ε is not a complex root of unity. It is natural to wonder whether ε is a fundamental unit of this order. It turns out that the answer is in general yes, and that a fundamental unit of this order can be explicitly given (as an explicit polynomial in ε) in the rare cases when the answer is no. This paper is a self-contained exposition of the solution to this problem, solution which was up to now scattered in many papers in the literature.},
author = {Stéphane R. Louboutin},
journal = {Banach Center Publications},
keywords = {fundamental units; orders; discriminants},
language = {eng},
number = {1},
pages = {173-189},
title = {Fundamental units for orders of unit rank 1 and generated by a unit},
url = {http://eudml.org/doc/286247},
volume = {108},
year = {2016},
}

TY - JOUR
AU - Stéphane R. Louboutin
TI - Fundamental units for orders of unit rank 1 and generated by a unit
JO - Banach Center Publications
PY - 2016
VL - 108
IS - 1
SP - 173
EP - 189
AB - Let ε be an algebraic unit for which the rank of the group of units of the order ℤ[ε] is equal to 1. Assume that ε is not a complex root of unity. It is natural to wonder whether ε is a fundamental unit of this order. It turns out that the answer is in general yes, and that a fundamental unit of this order can be explicitly given (as an explicit polynomial in ε) in the rare cases when the answer is no. This paper is a self-contained exposition of the solution to this problem, solution which was up to now scattered in many papers in the literature.
LA - eng
KW - fundamental units; orders; discriminants
UR - http://eudml.org/doc/286247
ER -