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Beta expansion of Salem numbers approaching Pisot numbers with the finiteness property

Volume 168 / 2015

Hachem Hichri Acta Arithmetica 168 (2015), 107-119 MSC: Primary 11R06, 11K16; Secondary 11Y99. DOI: 10.4064/aa168-2-2

Abstract

It is already known that all Pisot numbers are beta numbers, but for Salem numbers this was proved just for the degree 4 case. In 1945, R. Salem showed that for any Pisot number $\theta $ we can construct a sequence of Salem numbers which converge to $\theta $. In this short note, we give some results on the beta expansion for infinitely many sequences of Salem numbers obtained by this construction.

Authors

  • Hachem HichriInstitut préparatoire aux études d'ingénieur de Monastir
    Université de Monastir
    5019 Monastir, Tunisia
    e-mail

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