An arithmetical property of powers of Salem numbers

Toufik Zaïmi

doi:10.1016/j.jnt.2005.11.012

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An arithmetical property of powers of Salem numbers

Journal article

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Peer reviewed

An arithmetical property of powers of Salem numbers

Toufik Zaïmi

Journal of number theory, Vol.120(1), pp.179-191

01/09/2006

DOI: https://doi.org/10.1016/j.jnt.2005.11.012

Abstract

Fractional parts

Salem numbers

Let ζ be a nonzero real number and let α be a Salem number. We show that the difference between the largest and smallest limit points of the fractional parts of the numbers ζ α n , when n runs through the set of positive rational integers, can be bounded below by a positive constant depending only on α if and only if the algebraic integer α − 1 is a unit.

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Title: An arithmetical property of powers of Salem numbers
Creators - without role: Toufik Zaïmi - King Saud University
Publication Details: Journal of number theory, Vol.120(1), pp.179-191
Publisher: Elsevier Inc
Identifiers: 9916215508331
Academic Unit: Imam Mohammad Ibn Saud Islamic University (IMSIU)
Language: English
Resource Type: Journal article