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. We investigate what can be said about the smallest nonzero height of a degree $3$ totally $p$-adic number.

Keywords

Mathematical Subject Classification 2010

Supplementary material

Abelian cubic polynomials and congruence classes (mod $m_i$) for splitting over $mathbb{Q}_p$

Milestones

Authors