Salem numbers of degree four have periodic expansions. (English) Zbl 0685.12004

Théorie des nombres, C. R. Conf. Int., Québec/Can. 1987, 57-64 (1989).
[For the entire collection see Zbl 0674.00008.]
Suppose that \(\beta >1\) is a real number. Let T be the mapping \(Tx=\beta x mod 1\). A Salem number is an algebraic integer \(\beta >1\) each of whose other conjugates \(\gamma\) satisfies \(| \gamma | \leq 1\), with at least one \(| \gamma | =1\). It is proved that a Salem number of degree 4 is a periodic point of T and its \(\beta\)-expansion is determined explicitly.
Reviewer: F.Schweiger


11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11A63 Radix representation; digital problems


Zbl 0674.00008