Results 11 to 20 of about 48,005 (265)

Some results on a special type of real quadratic fields

Қарағанды университетінің хабаршысы. Математика сериясы, 2019
In this paper, we determine the real quadratic fields Q(√d ) coincide with positive square - free integers d including the continued fraction expansion form of wd = [a0 ; 7,7,…,7 l-1 , al].
Ö. ¨Özer, D. Bellaouar
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Beta-expansion and continued fraction expansion

Journal of Mathematical Analysis and Applications, 2008
For a real number \(\beta > 1\), every real number \(x \in [0,1]\) has a \(\beta\)-expansion \(x = \sum_{n=1}^\infty \varepsilon_n(x) \beta^{-n}\). Such \(\beta\)-expansions in general are non-unique, but letting \(T_\beta x = \{\beta x\}\), where \(\{y\}\) denotes the fractional part of \(y\), we obtain such an expansion where \(\varepsilon_n(x ...
Li, Bing, Wu, Jun
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A Wirsing-type approach to some continued fraction expansion

International Journal of Mathematics and Mathematical Sciences, 2005
Chan (2004) considered a certain continued fraction expansion and the corresponding Gauss-Kuzmin-Lévy problem. A Wirsing-type approach to the Perron-Frobenius operator of the associated transformation under its invariant measure allows us to obtain a ...
Gabriela Ileana Sebe
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Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction

Advances in Difference Equations, 2010
Yu. V. Nesterenko has proved that ζ(3)=b0+a1|/|b1+⋯+aν|/|bν+⋯, b0=b1=a2=2, a1=1,b2=4, b4k+1=2k+2, a4k+1=k(k+1), b4k+2=2k+4, and a4k+2=(k+1)(k+2) for k∈ℕ; b4k+3=2k+3, a4k+3=(k+1)2, and b4k+4=2k+2, a4k+
Leonid Gutnik
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Computer use in continued fraction expansions [PDF]

Mathematics of Computation, 1969
In this study, the use of computers is demonstrated for the rapid expansion of a general regular continued fraction with rational elements for √ C + L \surd C + L , where C C and L L are rational numbers, C C positive.
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LARGE DEVIATION ASYMPTOTICS FOR CONTINUED FRACTION EXPANSIONS [PDF]

Stochastics and Dynamics, 2008
We study large deviation asymptotics for processes defined in terms of continued fraction digits. We use the continued fraction digit sum process to define a stopping time and derive a joint large deviation asymptotic for the upper and lower fluctuation processes. Also a large deviation asymptotic for single digits is given.
Kesseböhmer, Marc, Slassi, Mehdi
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On the metrical theory of a non-regular continued fraction expansion

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015
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 ...
Lascu Dan, Cîrlig George
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Fundamental Solutions to Some Pell Equations

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2013
Let a,b and n are positive integers. In this paper, we find continued fraction expansion of ;#8730;d when d=a^2 b^2+2b, a^2 b^2+b,a^2±2,a^2±a. We will use continued fraction expansion of ;#8730;d in order to get the fundamental solutions to the equations
Merve Güney, Refik Keskin
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Some lacunarity properties of partial quotients of real numbers

Comptes Rendus. Mathématique
We consider lacunarity properties of sequence of partial quotients for real numbers in their continued fraction expansions. Hausdorff dimension of the sets of points with different lacunarity conditions on their partial quotients are calculated.
Zhao, Xuan, Zhang, Zhenliang
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On the Eventually Periodic Continued β-Fractions and Their Lévy Constants

Mathematics, 2022
In this paper, we consider continued β-fractions with golden ratio base β. We show that if the continued β-fraction expansion of a non-negative real number is eventually periodic, then it is the root of a quadratic irreducible polynomial with the ...
Qian Xiao, Chao Ma, Shuailing Wang
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