论文标题
完全p-adig的学位3
Totally p-adic Numbers of Degree 3
论文作者
论文摘要
代数数量$α$的高度是衡量算术复杂$α$的量度。我们说，如果$α$的最小多项式完全分配在$ \ mathbb {q} _p $ of $ p $ - addic数字上，则$α$完全是$ p $ - adic。在本文中，我们调查了关于$ 3 $ $ 3 $ $ p $ adadic的最小非零高度的说法。特别是，我们提供了一种算法来确定给定质量$ p $的最小高度$ 3 $ $ 3 $ $ p $ - 亚法数。
The height of an algebraic number $α$ is a measure of how arithmetically complicated $α$ is. We say $α$ is totally $p$-adic if the minimal polynomial of $α$ splits completely over the field $\mathbb{Q}_p$ of $p$-adic numbers. In this paper, we investigate what can be said about the smallest nonzero height of a degree $3$ totally $p$-adic number. In particular, we provide an algorithm to determine, given a prime $p$, the smallest height of a degree $3$ totally $p$-adic number.
