The infimum in the metric Mahler measure

Dubickas and Smyth defined the metric Mahler measure on the multiplicative group of non-zero algebraic numbers. The definition involves taking an infimum over representations of an algebraic number \(\alpha\) by other algebraic numbers. We verify their conjecture that the infimum in its definition i...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2014-08
Main Author: Samuels, Charles L
Format: Article
Language:English
Subjects:
Algebra
Infimum
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Dubickas and Smyth defined the metric Mahler measure on the multiplicative group of non-zero algebraic numbers. The definition involves taking an infimum over representations of an algebraic number \(\alpha\) by other algebraic numbers. We verify their conjecture that the infimum in its definition is always achieved as well as establish its analog for the ultrametric Mahler measure.
ISSN:2331-8422
DOI:10.48550/arxiv.1408.4165