Comments on the distribution modulo one of powers of Pisot and Salem numbers
Toufik Zaı̈mi · Publicationes Mathematicae Debrecen · 2012
We consider the sequence of distances to the nearest integer λα n , n = 1, 2, 3, . . ., where λ is a real number and α is a Salem number.We prove a characterization of the numbers λ satisfying the inequality lim sup n→∞ λα n < ε, where ε ∈ ]0, C(α)] and C(α) is the inverse of the length of the minimal polynomial of α.This allows us to extend a related result, on Salem numbers, due to A. H. Fan and J. Schmeling [5].