Equidistribution modulo 1 and Salem numbers
Doche, Christophe ; Mendès France, Michel ; Ruch, Jean-Jacques
Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, p. 261-271 / Harvested from Project Euclid
Let $\theta$ be a Salem number. It is well-known that the sequence $(\theta^n)$ 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 $\lim_{n\to\infty} n/s(n)$ over all equidistributed subsequences $(\theta^{s(n)})$. 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.
Publié le : 2008-12-15
Classification:  Salem number,  Equidistribution modulo 1,  $J_0$ Bessel function,  11K06,  11J71
@article{1229696575,
     author = {Doche, Christophe and Mend\`es France, Michel and Ruch, Jean-Jacques},
     title = {Equidistribution modulo 1 and Salem numbers},
     journal = {Funct. Approx. Comment. Math.},
     volume = {38},
     number = {1},
     year = {2008},
     pages = { 261-271},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229696575}
}
Doche, Christophe; Mendès France, Michel; Ruch, Jean-Jacques. Equidistribution modulo 1 and Salem numbers. Funct. Approx. Comment. Math., Tome 38 (2008) no. 1, pp.  261-271. http://gdmltest.u-ga.fr/item/1229696575/