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1
Content available remote On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm
100%
Komatsu T.
Acta Arithmetica
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1998
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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,...].
2
Content available remote A certain power series associatedwith a Beatty sequence
100%
Komatsu T.
Acta Arithmetica
|
1996
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tom 76
|
nr 2
109-129
3
Content available Leaping convergents of Tasoev continued fractions
100%
Komatsu T.
Discussiones Mathematicae - General Algebra and Applications
|
2011
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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.
4
Content available 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.
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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