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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-2-2,
author = {Hachem Hichri},
title = {Beta expansion of Salem numbers approaching Pisot numbers with the finiteness property},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {107-119},
zbl = {06429000},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-2-2}
}
Hachem Hichri. Beta expansion of Salem numbers approaching Pisot numbers with the finiteness property. Acta Arithmetica, Tome 168 (2015) pp. 107-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-2-2/