EQUIDISTRIBUTION MODULO 1 AND SALEM NUMBERS
Langue
en
Article de revue
Ce document a été publié dans
Functiones et Approximatio. 2008-06-16, vol. XXXIX, n° 2, p. 261–271
Résumé en anglais
Let θ be a Salem number. It is well-known that the sequence (θ n ) modulo 1 is dense but not equidistributed. In this article we discuss equidistributed subsequences. Our first approach is computational and consists in ...Lire la suite >
Let θ be a Salem number. It is well-known that the sequence (θ n ) 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 (θ s(n) ). As a result, we obtain an explicit upper bound onthe 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.< Réduire
Mots clés en anglais
Salem number
Equidistribution modulo 1
J0 Bessel function.
J0 Bessel function
Origine
Importé de halUnités de recherche