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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 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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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
doaj +2 more sources
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.
J. Rivat
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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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Martingale differences and the metric theory of continued fractions [PDF]
Illinois Journal of Mathematics, 2008 Illinois Journal of Mathematics ...
Haynes, AK, Vaaler, J
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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 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
H. Riesel
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Intermediate convergents and a metric theorem of Khinchin [PDF]
, 2009 A landmark theorem in the metric theory of continued fractions begins this way: Select a non‐negative real function f defined on the positive integers and a real number x, and form the partial sums sn of f evaluated at the partial quotients a1, …, an in ...
A. Haynes
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Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: Analytical approximation [PDF]
, 2017 Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. L\"u, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett.
Konstantinos D. Kokkotas +3 more
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