A lower bound for the height in abelian extensions
type: Item
instance of: scholarly article
title: A lower bound for the height in abelian extensions
zbMATH Open document ID: 0973.11092
author: Francesco Amoroso
author: Roberto Dvornicich
published in: Journal of Number Theory
publication date: 2001-10-29T00:00:00Z
review text: It is shown that if \(\alpha\neq 0\) is an element which is not a root of unity, of an abelian extension of the rationals, then its logarithmic height, \(h(\alpha)\) satisfies \(h(\alpha)\geq(\log 5)/12\). This is used to obtain lower bounds for norms and class-numbers in abelian extensions.
Mathematics Subject Classification ID: 11R06
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11G50
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 1423159
zbMATH Keywords: Weil's height
zbMATH Keywords: logarithmic height
zbMATH Keywords: abelian fields
zbMATH Keywords: Lehmer's problem
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: jnth.1999.2451
OpenAlex ID: W2064292613
cites work: Q5532660
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cites work: Q4101931
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cites work: Q3943047
DOI: 10.1006/JNTH.1999.2451
description: scientific article; zbMATH DE number 1423159