Equidistribution modulo 1 and salem numbers

Let θ be a Salem number. It is well-known that the sequence (θⁿ) modulo 1 is dense but not equidistributed. In this article we discuss equidistributed subsequences. Our first approach is computational and consists in estimating the supremum of lim_n→∞ n/s(n) over all equidistributed subsequences (θ^s(n)). As a result, we obtain an explicit upper bound on the density of any equidistributed subsequence. Our second approach is probabilistic. Defining a measure on the family of increasing integer sequences, we show that relatively to that measure, almost no subsequence is equiditributed.