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

Hachem Hichri. "Beta expansion of Salem numbers approaching Pisot numbers with the finiteness property." Acta Arithmetica 168.2 (2015): 107-119. <http://eudml.org/doc/279024>.

@article{HachemHichri2015,
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 θ we can construct a sequence of Salem numbers which converge to θ. In this short note, we give some results on the beta expansion for infinitely many sequences of Salem numbers obtained by this construction.},
author = {Hachem Hichri},
journal = {Acta Arithmetica},
keywords = {salem numbers; Pisot numbers; beta expansion; beta numbers; finiteness property},
language = {eng},
number = {2},
pages = {107-119},
title = {Beta expansion of Salem numbers approaching Pisot numbers with the finiteness property},
url = {http://eudml.org/doc/279024},
volume = {168},
year = {2015},
}

TY - JOUR
AU - Hachem Hichri
TI - Beta expansion of Salem numbers approaching Pisot numbers with the finiteness property
JO - Acta Arithmetica
PY - 2015
VL - 168
IS - 2
SP - 107
EP - 119
AB - 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 θ we can construct a sequence of Salem numbers which converge to θ. In this short note, we give some results on the beta expansion for infinitely many sequences of Salem numbers obtained by this construction.
LA - eng
KW - salem numbers; Pisot numbers; beta expansion; beta numbers; finiteness property
UR - http://eudml.org/doc/279024
ER -