Lehmer without Bogomolov
Fabien Pazuki, Niclas Technau, Martin Widmer
TL;DR
This paper constructs specific algebraic number fields that possess the Lehmer property but lack the Bogomolov property, addressing a recent open question in number theory.
Contribution
It provides explicit examples of fields with the Lehmer property but without the Bogomolov property, clarifying their relationship.
Findings
Existence of fields with Lehmer but not Bogomolov property
Answers a recent open question in algebraic number theory
Advances understanding of properties of algebraic number fields
Abstract
We construct fields of algebraic numbers that have the Lehmer property but not the Bogomolov property. This answers a recent implicit question of Pengo and the first author.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation