Equidistribution modulo 1 and salem numbers

Christophe Doche, Michel Mendès France, Jean Jacques Ruch

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)261-271
Number of pages11
JournalFunctiones et Approximatio, Commentarii Mathematici
Volume39
Issue number2
Publication statusPublished - 2008

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