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Mahler Measures Close to an Integer

Published online by Cambridge University Press:  20 November 2018

Artūras Dubickas
Artūras Dubickas*
Affiliation:
Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania, e-mail: [email protected] website: http://www.mif.vu.lt/ttsk/bylos/da/da_a.html
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Abstract

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We prove that the Mahler measure of an algebraic number cannot be too close to an integer, unless we have equality. The examples of certain Pisot numbers show that the respective inequality is sharp up to a constant. All cases when the measure is equal to the integer are described in terms of the minimal polynomials.

Keywords

11R0411R0611R0911J68Mahler measurePV numbersSalem numbers
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 196 - 203
Copyright
Copyright © Canadian Mathematical Society 2002

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