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• 1 Vilnius University Department of Mathematics and Informatics Naugarduko 24 Vilnius 2600 Lithuania E-mail Naugarduko 24 Vilnius 2600 Lithuania E-mail
• | 2 Edinburgh, University, J.C.M.B School of Mathematics King's Buildings Mayfield Road, Edinburgh EH9 3JZ Scotland UK E-mail King's Buildings Mayfield Road, Edinburgh EH9 3JZ Scotland UK E-mail
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## 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.

Manuscript Submission: HERE

• Impact Factor (2019): 0.693
• Scimago Journal Rank (2019): 0.412
• SJR Hirsch-Index (2019): 20
• SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
• Impact Factor (2018): 0.664
• Scimago Journal Rank (2018): 0.412
• SJR Hirsch-Index (2018): 19
• SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1971
Volumes
per Year
2
Issues
per Year
4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Springer Nature Switzerland AG
Publisher's
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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