Boyd, David W. 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 Cited in 4 ReviewsCited in 15 Documents MSC: 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure 11A63 Radix representation; digital problems Keywords:radix expansion; digital properties; Salem number Citations:Zbl 0674.00008 PDFBibTeX XML