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arXiv · 2009.01795

Totally p-adic Numbers of Degree 3

Emerald Stacy
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Abstract

The height of an algebraic number $\alpha$ is a measure of how arithmetically complicated $\alpha$ is. We say $\alpha$ is totally $p$-adic if the minimal polynomial of $\alpha$ 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.

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Emerald Stacy. 2020-09-03. Totally p-adic Numbers of Degree 3. https://arxiv.org/abs/2009.01795

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