On the multiples of a badly approximable vector

• Autorzy: Yann Bugeaud
• Języki publikacji: EN

Abstrakty

EN

Let d be a positive integer and α a real algebraic number of degree d + 1. Set $α̲:= (α,α²,...,α^{d})$. It is well-known that
$c(α̲) := lim inf_{q→ ∞} q^{1/d}·||qα̲|| > 0$,
where ||·|| denotes the distance to the nearest integer. Furthermore,
$c(α̲)n^{-1/d} ≤ c(nα̲) ≤ nc(α̲)$
for any integer n ≥ 1. Our main result asserts that there exists a real number C, depending only on α, such that
$c(nα̲) ≤ Cn^{-1/d}$
for any integer n ≥ 1.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 168
• Numer: 1
• Strony: 71-81

Daty

wydano

2015

Twórcy

autor

Yann Bugeaud

• Université de Strasbourg, Mathématiques, 7, rue René Descartes, 67084 Strasbourg Cedex, France

Identyfikatory

DOI

10.4064/aa168-1-4