Density of some sequences modulo 1

Artūras Dubickas. "Density of some sequences modulo 1." Colloquium Mathematicae 128.2 (2012): 237-244. <http://eudml.org/doc/283548>.

@article{ArtūrasDubickas2012,
abstract = {Recently, Cilleruelo, Kumchev, Luca, Rué and Shparlinski proved that for each integer a ≥ 2 the sequence of fractional parts $\{aⁿ/n\}_\{n=1\}^\{∞\}$ is everywhere dense in the interval [0,1]. We prove a similar result for all Pisot numbers and Salem numbers α and show that for each c > 0 and each sufficiently large N, every subinterval of [0,1] of length $cN^\{-0.475\}$ contains at least one fractional part Q(αⁿ)/n, where Q is a nonconstant polynomial in ℤ[z] and n is an integer satisfying 1 ≤ n ≤ N.},
author = {Artūras Dubickas},
journal = {Colloquium Mathematicae},
keywords = {distribution modulo 1; gaps between primes},
language = {eng},
number = {2},
pages = {237-244},
title = {Density of some sequences modulo 1},
url = {http://eudml.org/doc/283548},
volume = {128},
year = {2012},
}

TY - JOUR
AU - Artūras Dubickas
TI - Density of some sequences modulo 1
JO - Colloquium Mathematicae
PY - 2012
VL - 128
IS - 2
SP - 237
EP - 244
AB - Recently, Cilleruelo, Kumchev, Luca, Rué and Shparlinski proved that for each integer a ≥ 2 the sequence of fractional parts ${aⁿ/n}_{n=1}^{∞}$ is everywhere dense in the interval [0,1]. We prove a similar result for all Pisot numbers and Salem numbers α and show that for each c > 0 and each sufficiently large N, every subinterval of [0,1] of length $cN^{-0.475}$ contains at least one fractional part Q(αⁿ)/n, where Q is a nonconstant polynomial in ℤ[z] and n is an integer satisfying 1 ≤ n ≤ N.
LA - eng
KW - distribution modulo 1; gaps between primes
UR - http://eudml.org/doc/283548
ER -