论文标题
加权高度的相对诺斯科特数字
Relative Northcott numbers for the weighted Weil heights
论文作者
论文摘要
计算高度函数的下限是基本的基础。灰色在相对环境中研究了Weil高度的下限。 VIDAUX和VIDELA引入了northcott编号，以设置$ a \ subset \ bar {\ mathbb {q}}} $。它从下方，零高点和有限的许多小高点之外的$ a $ a $ a $ a $ a限制。 Pazuki，Technau和Widmer引入了加权的Weil高度。这些高度概括了绝对和相对的高度。在本文中，我们介绍了与加权Weil高度有关的Northcott号码的相对版本。我们还提供了一个场扩展，其诺斯科特数量等于给定的正数。这项工作是作者和萨诺（Sano）在诺斯科特（Northcott）数字上的相对版本，用于加权的高度。
It is fundamental in number theory to calculate lower bounds for height functions. Grizzard studied lower bounds for the Weil height in a relative setting. Vidaux and Videla introduced the Northcott number for a set $A\subset\bar{\mathbb{Q}}$. It bounds the Weil height on $A$ from below, outside the zero-height points and the finitely many small-height points. Pazuki, Technau, and Widmer introduced the weighted Weil heights. These heights generalize both the absolute and relative Weil heights. In this paper, we introduce a relative version of the Northcott number related to the weighted Weil height. We also give a field extension whose Northcott number equals a given positive number. The work is a relative version of the previous work of the author and Sano on the Northcott numbers for the weighted Weil heights.
