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On the beta expansion of Salem numbers of degree 8

Part of: Algebraic number theory: global fields Probabilistic theory: distribution modulo $1$; metric theory of algorithms Computational number theory

Published online by Cambridge University Press:  01 June 2014

Hachem Hichri
Hachem Hichri*
Affiliation:
Departement de Mathematiques (UR11ES50), Faculté des sciences de Monastir , Université de Monastir, Monastir 5019, Tunisie email hichemhichri@yahoo.fr

Abstract

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Boyd showed that the beta expansion of Salem numbers of degree 4 were always eventually periodic. Based on an heuristic argument, Boyd had conjectured that the same is true for Salem numbers of degree 6 but not for Salem numbers of degree 8. This paper examines Salem numbers of degree 8 and collects experimental evidence in support of Boyd’s conjecture.

MSC classification

Secondary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure 11Y99: None of the above, but in this section
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 289 - 301
Copyright
© The Author 2014 

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