Displaying similar documents to “The integral mean of the sum-of-digits function of the Ostrowski expansion”

Generalized golden ratios of ternary alphabets

Vilmos Komornik, Anna Chiara Lai, Marco Pedicini (2011)

Journal of the European Mathematical Society

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Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases...

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

Hachem Hichri (2015)

Acta Arithmetica

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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.