Vol. 4, No. 1, 2020

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Totally $p$-adic numbers of degree 3

Emerald Stacy

Vol. 4 (2020), No. 1, 387–401
Abstract

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 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
height, algorithm, $p$-adic
Mathematical Subject Classification 2010
Primary: 11G50, 11S20, 11Y40, 12Y05
Supplementary material

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

Milestones
Received: 23 February 2020
Revised: 1 August 2020
Accepted: 29 August 2020
Published: 29 December 2020
Authors
Emerald Stacy
Mathematics and Computer Science
Washington College
Chestertown, MD
United States