no. 6
Number theory
On the distribution modulo 1 of the sum of powers of a Salem number
[Sur la répartition modulo 1 de la somme des puissances d'un nombre de Salem]

Présenté par : Jean-Pierre Serre

Stankov, Dragan1
1 Katedra Matematike RGF-a, University of Belgrade, Beograd, Đušina 7, Serbia
Comptes Rendus. Mathématique, Tome 354 (2016) no. 6, pp. 569-576.

Il est bien connu que la suite des puissances d'un nombre de Salem θ, modulo 1, est dense dans l'intervalle unité, sans être uniformément distribuée. Généralisant un résultat de Dupain, on détermine explicitement la fonction de répartition de la suite (P(θn)mod 1)n≥1, où P est un polynôme à coefficients entiers et θ est quartique. On illustre également la méthode de détermination par quelques exemples.

It is well known that the sequence of powers of a Salem number θ, modulo 1, is dense in the unit interval, but is not uniformly distributed. Generalizing a result of Dupain, we determine, explicitly, the repartition function of the sequence (P(θn)mod 1)n≥1, where P is a polynomial with integer coefficients and θ is quartic. Also, we consider some examples to illustrate the method of determination.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.03.012
Stankov, Dragan 1

1 Katedra Matematike RGF-a, University of Belgrade, Beograd, Đušina 7, Serbia 
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Stankov, Dragan. On the distribution modulo 1 of the sum of powers of a Salem number. Comptes Rendus. Mathématique, Tome 354 (2016) no. 6, pp. 569-576. doi : 10.1016/j.crma.2016.03.012. http://www.numdam.org/articles/10.1016/j.crma.2016.03.012/

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