Density of some sequences modulo 1

• Autorzy: Artūras Dubickas
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11K06: General theory of distribution modulo 1
• 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
• 11K31: Special sequences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 128
• Numer: 2
• Strony: 237-244

Daty

wydano

2012

Twórcy

autor

Artūras Dubickas

• Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania

Identyfikatory

DOI

10.4064/cm128-2-9