On the S-Euclidean minimum of an ideal class

Kevin J. McGown. "On the S-Euclidean minimum of an ideal class." Acta Arithmetica 171.2 (2015): 125-144. <http://eudml.org/doc/279037>.

@article{KevinJ2015,
abstract = {We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from ergodic theory and topological dynamics, particularly those of Berend.},
author = {Kevin J. McGown},
journal = {Acta Arithmetica},
keywords = {Euclidean ring; euclidean ideal; Euclidean minimum; conjecture of Barnes and Swinnerton-Dyer},
language = {eng},
number = {2},
pages = {125-144},
title = {On the S-Euclidean minimum of an ideal class},
url = {http://eudml.org/doc/279037},
volume = {171},
year = {2015},
}

TY - JOUR
AU - Kevin J. McGown
TI - On the S-Euclidean minimum of an ideal class
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 2
SP - 125
EP - 144
AB - We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from ergodic theory and topological dynamics, particularly those of Berend.
LA - eng
KW - Euclidean ring; euclidean ideal; Euclidean minimum; conjecture of Barnes and Swinnerton-Dyer
UR - http://eudml.org/doc/279037
ER -