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# On metric heights

Periodica Mathematica Hungarica
Authors: A. Dubickas and C. Smyth

## Abstract

Metric heights are modified height functions on the non-zero algebraic numbers Q which can be used to define a metric on certain cosets of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\overline {\mathbb{Q}} ^*$$ \end{document}
. They have been defined with a view to eventually applying geometric methods to the study of
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\overline {\mathbb{Q}} ^*$$ \end{document}
. In this paper we discuss the construction of metric heights in general. More specifically, we study in some detail the metric height obtained from the na"ve height of an algebraic number (the maximum modulus of the coefficients of its minimal polynomial). In particular, we compute this metric height for some classes of surds.
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# Some inequalities for certain power sums

Acta Mathematica Hungarica
Author: C. J. Smyth
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