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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Leaping convergents of Tasoev continued fractions

100%
Komatsu T.
Discussiones Mathematicae - General Algebra and Applications
|
2011
|
tom 31
|
nr 2
201-216
EN
Denote the n-th convergent of the continued fraction by pₙ/qₙ = [a₀;a₁,...,aₙ]. We give some explicit forms of leaping convergents of Tasoev continued fractions. For instance, [0;ua,ua²,ua³,...] is one of the typical types of Tasoev continued fractions. Leaping convergents are of the form $p_{rn+i}/q_{rn+i}$ (n=0,1,2,...) for fixed integers r ≥ 2 and 0 ≤ i ≤ r-1.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Leaping convergents of Hurwitz continued fractions

100%
Komatsu T.
Discussiones Mathematicae - General Algebra and Applications
|
2011
|
tom 31
|
nr 1
101-121
EN
Let pₙ/qₙ = [a₀;a₁,...,aₙ] be the n-th convergent of the continued fraction expansion of [a₀;a₁,a₂,...]. Leaping convergents are those of every r-th convergent $p_{rn+i}/q_{rn+i}$ (n = 0,1,2,...) for fixed integers r and i with r ≥ 2 and i = 0,1,...,r-1. The leaping convergents for the e-type Hurwitz continued fractions have been studied. In special, recurrence relations and explicit forms of such leaping convergents have been treated. In this paper, we consider recurrence relations and explicit forms of the leaping convergents for some different types of Hurwitz continued fractions.
3
Content available remote

On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm

100%
Komatsu T.
Acta Arithmetica
|
1998
|
tom 86
|
nr 4
305-324
EN
We obtain the values concerning $𝓜 (θ,ϕ) = lim inf_{|q| → ∞} |q| ‖qθ - ϕ‖$ using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values 𝓜 (θ,1/2), 𝓜 (θ,1/a), 𝓜 (θ,1/√(ab(ab+4))) and so on when θ = (√(ab(ab+4)) - ab)/(2a) = [0;a,b,a,b,...].
4
Content available remote

A certain power series associatedwith a Beatty sequence

100%
Komatsu T.
Acta Arithmetica
|
1996
|
tom 76
|
nr 2
109-129
5
Content available remote

On Hurwitzian and Tasoev's continued fractions

75%
Komatsu T.
Acta Arithmetica
|
2003
|
tom 107
|
nr 2
161-177
6
Content available remote

Generalized poly-Cauchy polynomials and their interpolating functions

51%
Komatsu T., Luca F., Pita Ruiz V. C.
Colloquium Mathematicum
|
2014
|
tom 136
|
nr 1
13-30
EN
We give a generalization of poly-Cauchy polynomials and investigate their arithmetical and combinatorial properties. We also study the zeta functions which interpolate the generalized poly-Cauchy polynomials.
7
Content available remote

Independence measures of arithmetic functions II

51%
Komatsu T., Laohakosol V., Ruengsinsub P.
Acta Arithmetica
|
2012
|
tom 153
|
nr 2
199-216
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