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Some quadratic irrationals with explicit continued fraction and Engel series expansions

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 52: Issue 3
DOI:
https://doi.org/10.1556/012.2015.52.3.1312
Authors: Narakorn Rompurk Kanasri, Vichian Laohakosol, and Tawat Changphas

–New York–Oxford, 1988 . [12] Tamura , J. , Explicit formulae for Cantor series representing quadratic irrationals , Number Theory

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Linear independence results for the reciprocal sums of Fibonacci numbers associated with Dirichlet characters

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 54: Issue 1
DOI:
https://doi.org/10.1556/012.2017.54.1.1354
Authors: Hiromi Ei, Florian Luca, and Yohei Tachiya

irrational values for rational values of the argument , Proc. Nat. Inst. Sci. India 13 ( 1947 ), 171 – 173 . [5] Duverney , D. , Nishioka , K

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Asymptotic behavior of the irrational factor

Acta Mathematica Hungarica
Volume/Issue:
Volume 121: Issue 3
DOI:
https://doi.org/10.1007/s10474-008-7212-9
Authors: E. Alkan, A. Ledoan, and A. Zaharescu

Abstract  

We study the irrational factor function I(n) introduced by Atanassov and defined by

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$I(n) = \prod\nolimits_{\nu = 1}^k {p_\nu ^{1/\alpha _\nu } }$$ \end{document}
, where
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$n = \prod\nolimits_{\nu = 1}^k {p_\nu ^{\alpha _\nu } }$$ \end{document}
is the prime factorization of n. We show that the sequence {G(n)/n}n≧1, where G(n) = Πν=1 n I(ν)1/n, is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function I(n).

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Irrational Rotations and Differentiability

Acta Mathematica Hungarica
Volume/Issue:
Volume 78: Issue 4
DOI:
https://doi.org/10.1023/a:1006595125719
Authors: Z. Buczolich, U. Darji, and R. O'Malley
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On the Irrationality of Certain Series

Periodica Mathematica Hungarica
Volume/Issue:
Volume 38: Issue 1-2
DOI:
https://doi.org/10.1023/a:1004742930674
Authors: Yong-Gao Chen and Imre Ruzsa
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The lévy constant of an irrational number

Acta Mathematica Hungarica
Volume/Issue:
Volume 74: Issue 1-2
DOI:
https://doi.org/10.1007/bf02697876
Author: C. Faivre
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Controlling Orthogonal Series with Irrational Rotations

Periodica Mathematica Hungarica
Volume/Issue:
Volume 38: Issue 1-2
DOI:
https://doi.org/10.1023/a:1004771704266
Author: Michel Weber
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Sur les Propriétés Arithmétiques de la Fonction de Tschakaloff

Periodica Mathematica Hungarica
Volume/Issue:
Volume 35: Issue 3
DOI:
https://doi.org/10.1023/a:1004509314381
Author: Daniel Duverney
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A space C p (X) is dominated by irrationals if and only if it is K-analytic

Acta Mathematica Hungarica
Volume/Issue:
Volume 107: Issue 4
DOI:
https://doi.org/10.1007/s10474-005-0194-y
Author: Vladimir V. Tkachuk

Summary We prove that, for any Tychonoff  X, the space C p(X) is K-analytic if and only if it has a compact cover {K p: p ? ??} such that K p subset K q whenever p,q ? ?? and p = q. Applying this result we show that if C p(X) is K-analytic then C p(?X) is K-analytic as well. We also establish that a space C p(X) is K-analytic and Baire if and only if X is countable and discrete.

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Some metrical observations on the approximation of an irrational number by its nearest mediants

Periodica Mathematica Hungarica
Volume/Issue:
Volume 23: Issue 1
DOI:
https://doi.org/10.1007/bf02260389
Author: H. Jager
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