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 limn→∞ n/s(n) over all equidistributed subsequences (θs(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.
|Number of pages||11|
|Journal||Functiones et Approximatio, Commentarii Mathematici|
|Publication status||Published - 2008|