On the S-Euclidean minimum of an ideal class
Number Theory
2013-08-13 v2
Abstract
We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. We also 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. The proof is self-contained but uses ideas from ergodic theory and topological dynamics, particularly those of Berend.
Keywords
Cite
@article{arxiv.1304.1815,
title = {On the S-Euclidean minimum of an ideal class},
author = {Kevin J. McGown},
journal= {arXiv preprint arXiv:1304.1815},
year = {2013}
}