论文标题
大型代数整数
Large Algebraic Integers
论文作者
论文摘要
如果代数整数的所有真实或复杂的嵌入式具有绝对值大于$ 1 $，则表示很大。如果\ emph {大}允许一个大发电机，则说一个整体理想。我们研究了宽敞的概念，将其与所涉及的一些算术不变性有关，例如调节器和单位晶格的覆盖半径。我们还研究了它与Weil高度和Bogomolov属性的联系。我们提供了一种用于测试宽敞性的算法，并为持续分数理论引起的地板功能的构建提供了一些应用。
An algebraic integer is said large if all its real or complex embeddings have absolute value larger than $1$. An integral ideal is said \emph{large} if it admits a large generator. We investigate the notion of largeness, relating it to some arithmetic invariants of the field involved, such as the regulator and the covering radius of the lattice of units. We also study its connection with the Weil height and the Bogomolov property. We provide an algorithm for testing largeness and give some applications to the construction of floor functions arising in the theory of continued fractions.
