论文标题
单位还原的字段和完美的单一形式
Unit Reducible Fields and Perfect Unary Forms
论文作者
论文摘要
在本文中，我们介绍了数字字段降低单位的概念，即数字字段，其中所有阳性一单位形式在一个单位处达到其非零最小值。此外，我们研究了给定数字字段的单位降低性和同一个类别的完美一类形式的链接，并证明了D. Yasaki在真实二次领域中关于完美一类形式的类别的开放猜想。
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.
