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On decimal and continued fraction expansions of a real number

100%

Faivre C.

Acta Arithmetica

1997

tom 82

nr 2

119-128

On the central limit theorem for random variables related to the continued fraction expansion

100%

Faivre C.

Colloquium Mathematicum

1996

tom 71

nr 1

153-159

Sur la somme des quotients partiels du développement en fraction continue

63%

Barbolosi D., Faivre C.

Colloquium Mathematicum

2001

tom 89

nr 2

159-167

Let [0;a₁(x),a₂(x),…] be the regular continued fraction expansion of an irrational x ∈ [0,1]. We prove mainly that, for α > 0, β ≥ 0 and for almost all x ∈ [0,1], $lim_{n→∞} (aⁿ₁(x) + … + aⁿₙ(x))/nlogn = α/log2$ if α < 1 and β ≥ 0, $lim_{n→∞} (aⁿ₁(x) + … + aⁿₙ(x))/nlogn = 1/log2$ if α = 1 and β < 1, and, if α > 1 or α = 1 and β >1, $lim inf_{n→∞} (aⁿ₁(x) + … + aⁿₙ(x))/nlogn = 1/log2$, $lim sup_{n→∞} (aⁿ₁(x) + … + aⁿₙ(x))/nlogn = ∞$, where $aⁿ_{i}(x) = a_{i}(x)$ if $a_{i}(x) ≤ n^{α}log^{β}n$ and $aⁿ_{i}(x) = 0$ otherwise, for all i ∈ {1,…,n}.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Acta Arithmetica

3 Faivre C.

1 Barbolosi D.

1 2001

1 1997

1 1996

Wyniki wyszukiwania

On decimal and continued fraction expansions of a real number

On the central limit theorem for random variables related to the continued fraction expansion

Sur la somme des quotients partiels du développement en fraction continue