Linear relations with conjugates of a Salem number

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Linear relations with conjugates of a Salem number. / Dubickas, Artūras; Jankauskas, Jonas.
in: Journal de théorie des nombres de Bordeaux, Jahrgang 32.2020, Nr. 1, 2020, S. 179–191.

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

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@article{7b56ba89b38b4c39ae175367bca72dc6,
title = "Linear relations with conjugates of a Salem number",
abstract = " In this paper we consider linear relations with conjugates of a Salem number$\alpha$. We show that every such a relation arises from a linear relationbetween conjugates of the corresponding totally real algebraic integer$\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem numberwith a nontrivial relation between its conjugates is $8$, whereas the smallestlength of a nontrivial linear relation between the conjugates of a Salem numberis $6$.",
keywords = "Additive linear relations, Salem numbers, Pisot numbers, Totally real algebraic numbers",
author = "Artūras Dubickas and Jonas Jankauskas",
year = "2020",
language = "English",
volume = "32.2020",
pages = "179–191",
journal = "Journal de th{\'e}orie des nombres de Bordeaux",
issn = "1246-7405",
publisher = "Universite de Bordeaux III (Michel de Montaigne)",
number = "1",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Linear relations with conjugates of a Salem number

AU - Dubickas, Artūras

AU - Jankauskas, Jonas

PY - 2020

Y1 - 2020

N2 - In this paper we consider linear relations with conjugates of a Salem number$\alpha$. We show that every such a relation arises from a linear relationbetween conjugates of the corresponding totally real algebraic integer$\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem numberwith a nontrivial relation between its conjugates is $8$, whereas the smallestlength of a nontrivial linear relation between the conjugates of a Salem numberis $6$.

AB - In this paper we consider linear relations with conjugates of a Salem number$\alpha$. We show that every such a relation arises from a linear relationbetween conjugates of the corresponding totally real algebraic integer$\alpha+1/\alpha$. It is also shown that the smallest degree of a Salem numberwith a nontrivial relation between its conjugates is $8$, whereas the smallestlength of a nontrivial linear relation between the conjugates of a Salem numberis $6$.

KW - Additive linear relations

KW - Salem numbers

KW - Pisot numbers

KW - Totally real algebraic numbers

M3 - Article

VL - 32.2020

SP - 179

EP - 191

JO - Journal de théorie des nombres de Bordeaux

JF - Journal de théorie des nombres de Bordeaux

SN - 1246-7405

IS - 1

ER -