Let d≥ 1 be an integer and r=(r0,..., rd− 1)∈ Rd. The shift radix system τr: Zd→ Zd is defined
by τr (z)=(z1,..., zd− 1,−⌊ rz⌋) t (z=(z0,..., zd− 1) t). τr has the finiteness property if each z∈ …

In this article I state and prove some basic results about Salem numbers, and then survey
some of the literature about them. My intention is to complement other general treatises on …

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 …

A beta expansion is the analogue of the base 10 representation of a real number, where the
base may be a non-integer. Although the greedy beta expansion of 1 using a non-integer …

Let β> 1 be a real number and x∈[0, 1) be an irrational number. Denote by kn (x) the exact
number of partial quotients in the continued fraction expansion of x given by the first n digits …

The set of Salem numbers is proved to be bounded from below by $\theta_ {31}^{-1}=
1.08544\ldots $ where $\theta_ {n} $, $ n\geq 2$, is the unique root in $(0, 1) $ of the …

In this paper, we construct some families of polynomials defining Salem numbers which
approach integer numbers and we give some results on their beta expansion. As a …

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 …

The Conjecture of Lehmer is proved to be true. The proof mainly relies upon:(i) the
properties of the Parry Upper functions $ f_ {\house {\alpha}}(z) $ associated with the …

In this article I state and prove some basic results about Salem numbers, and then survey
some of the literature about them. My intention is to complement other general treatises on …