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Continued $\mathbf{A_2}$-fractions and singular functions
Математичні Студії, 2022 In the article we deepen the metric component of theory of infinite $A_2$-continued fractions $[0;a_1,a_2,...,a_n,...]$ with a two-element alphabet $A_2=\{\frac12,1\}$, $a_n\in A_2$ and establish the normal property of numbers of the segment $I=[\frac12 ...
M.V. Pratsiovytyi +3 more
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On the Quantitative Metric Theory of Continued Fractions in Positive Characteristic [PDF]
Proceedings of the Edinburgh Mathematical Society, 2018 AbstractLet 𝔽q be the finite field of q elements. An analogue of the regular continued fraction expansion for an element α in the field of formal Laurent series over 𝔽q is given uniquely by $$\alpha = A_0(\alpha ) + \displaystyle{1 \over {A_1(\alpha ) + \displaystyle{1 \over {A_2(\alpha ) + \ddots }}}},$$ where $(A_{n}(\alpha))_{n=0}^{\infty}$ is a ...
Lertchoosakul, Poj, Nair, Radhakrishnan
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On the metric theory of continued fractions [PDF]
Colloquium Mathematicum, 1998 For a positive integer \(n\), let \(P(n)\) be the measure of the set of irrational numbers \(x\in(0,1)\) such that the best approximation of \(x\) with denominator \(\leq n\) is a convergent of the continued fraction expansion of \(x\). The authors show \[ P(n)={1\over 2}+{6\over\pi^2}(\log 2)^2+O\left({1\over n}\right).
Aliev, I., Kanemitsu, S., Schinzel, A.
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ON THE METRIC THEORY OF CONTINUED FRACTIONS IN POSITIVE CHARACTERISTIC [PDF]
Mathematika, 2014 Let \(\mathbb{F}_q\) be the finite field of \(q\) elements. Denote by \(\mathbb{F}_q[Z]\) and \(\mathbb{F}_q(Z)\) the ring of polynomials (with coefficients in \(\mathbb{F}_q\)) and its fraction field. The field \(\mathbb{F}_q((Z^{-1}))\) of formal Laurent series, which is non-Archimedean and of positive characteristic, is the completion of \(\mathbb{F}
Lertchoosakul, Poj, Nair, Radhakrishnan
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On the Metrical Theory of Continued Fractions [PDF]
Proceedings of the American Mathematical Society, 1994 Suppose b k {b_k} denotes either ϕ ( k ) \phi (k) or ϕ ( p k ) ( k = 1 , 2 , … ) \phi ({p_k})\;(k = 1 ...
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Quantitative metric theory of continued fractions
Proceedings - Mathematical Sciences, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hančl, Jaroslav +3 more
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On the metric theory of continued fractions [PDF]
Colloquium Mathematicum, 1999 Denote by \(P(n)\) the Lebesgue measure of the set of all irrational numbers \(x\in (0,1)\) whose closest rational approximation with denominator \(\leq n\) is a convergent of the continued fraction of \(x\). Improving an earlier result [cf. \textit{I. Aliev}, \textit{S. Kanemitsu} and \textit{A. Schinzel}, Colloq. Math.
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On the metrical theory of a non-regular continued fraction expansion [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2015 Abstract We introduced a new continued fraction expansions in our previous paper. For these expansions, we show the Brodén-Borel-Lévy type formula. Furthermore, we compute the transition probability function from this and the symbolic dynamical system of the natural number with the unilateral shift.
Lascu Dan, Cîrlig George
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Martingale differences and the metric theory of continued fractions
Illinois Journal of Mathematics, 2008 Illinois Journal of Mathematics ...
Haynes, AK, Vaaler, J
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On the metric theory of nearest integer continued fractions [PDF]
BIT, 1987 The first part of this paper is a short introduction to some results, such as P. Lévy's and Khintchine's, in the metrical theory of continued fraction expansions. References are to Khintchine's well-known book from 1935, an excellent introduction in its days, but since the work of W. Doeblin (1940) and C. Ryll-Nardzewski (1951) who revealed the ergodic
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