Unit Reducible Fields and Perfect Unary Forms
Number Theory
2022-08-02 v2 Commutative Algebra
Abstract
In this paper, we introduce the notion of unit reducibility for number fields, that is, number fields in which all positive unary forms attain their nonzero minimum at a unit. Furthermore, we investigate the link between unit reducibility and the number of homothety classes of perfect unary forms for a given number field, and prove an open conjecture about the number of classes of perfect unary forms in real quadratic fields, stated by D. Yasaki.
Cite
@article{arxiv.2207.06385,
title = {Unit Reducible Fields and Perfect Unary Forms},
author = {Alar Leibak and Christian Porter and Cong Ling},
journal= {arXiv preprint arXiv:2207.06385},
year = {2022}
}
Comments
23 pages including appendix