Periodic Karyon Expansions of Algebraic Units in Multidimensional Continued Fractions
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DOI: 10.1007/s10958-017-3505-2
Abstract: Periodic expansions of algebraic numbers in multidimensional continued fractions are obtained by using multidimensional backward maps and a method for differentiating induced toric tilings. read more here.
Keywords: karyon expansions; expansions algebraic; continued fractions; periodic karyon ... See more keywords
Coset diagrams of the modular group and continued fractions
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DOI: 10.1016/j.crma.2019.07.002
Abstract: Abstract The coset diagram for each orbit under the action of the modular group on Q ( n ) ⁎ = Q ( n ) ∪ { ∞ } contains a circuit C i .… read more here.
Keywords: modular group; continued fractions; coset diagrams; circuit ... See more keywords
On quadratic approximation for hyperquadratic continued fractions
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DOI: 10.1016/j.jnt.2020.02.008
Abstract: Abstract We study quadratic approximations for two families of hyperquadratic continued fractions in the field of Laurent series over a finite field. As the first application, we give the answer to a question of the… read more here.
Keywords: quadratic approximation; continued fractions; approximation hyperquadratic; hyperquadratic continued ... See more keywords
TRANSCENDENTAL RUBAN p-ADIC CONTINUED FRACTIONS
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DOI: 10.1017/s0004972724000959
Abstract: We establish explicit constructions of Mahler’s p-adic $U_{m}$ -numbers by using Ruban p-adic continued fraction expansions of algebraic irrational p-adic numbers of degree m. read more here.
Keywords: transcendental ruban; continued fractions; ruban adic; adic continued ... See more keywords
THE MULTIFRACTAL SPECTRUM OF CONTINUED FRACTIONS WITH NONDECREASING PARTIAL QUOTIENTS
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DOI: 10.1017/s0004972724001011
Abstract: Let $[a_1(x),a_2(x),\ldots ,a_n(x),\ldots ]$ be the continued fraction expansion of $x\in [0,1)$ and $q_n(x)$ be the denominator of its nth convergent. The irrationality exponent and Khintchine exponent of x are respectively defined by $$ \begin{align*}… read more here.
Keywords: fractions nondecreasing; nondecreasing partial; log; partial quotients ... See more keywords
Approximating the nuclear binding energy using analytic continued fractions
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DOI: 10.1038/s41598-024-61389-5
Abstract: Understanding nuclear behaviour is fundamental in nuclear physics. This paper introduces a data-driven approach, Continued Fraction Regression (cf-r), to analyze nuclear binding energy (B(A, Z)). Using a tailored loss function and analytic continued fractions, our… read more here.
Keywords: analytic continued; nuclear binding; continued fractions; energy using ... See more keywords
Polynomial continued fractions for exp(π)
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DOI: 10.1080/10236198.2023.2204979
Abstract: We present two (inequivalent) polynomial continued fraction representations of the number eπ with all their elements in Q; no such representation was seemingly known before. More generally, a similar result for erπ is obtained for… read more here.
Keywords: continued fraction; fractions exp; polynomial continued; continued fractions ... See more keywords
The dynamics of Super-Apollonian continued fractions
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DOI: 10.1090/tran/7372
Abstract: We examine a pair of dynamical systems on the plane induced by a pair of spanning trees in the Cayley graph of the Super-Apollonian group of Graham, Lagarias, Mallows, Wilks, and Yan. The dynamical systems… read more here.
Keywords: apollonian continued; continued fractions; dynamical systems; dynamics super ... See more keywords
On the periodicity of continued fractions in elliptic fields
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DOI: 10.1134/s1064562417040068
Abstract: Article [1] raised the question of the finiteness of the number of square-free polynomials f ∈ ℚ[h] of fixed degree for which $$\sqrt f $$f has periodic continued fraction expansion in the field ℚ((h)) and… read more here.
Keywords: continued fractions; periodicity continued; elliptic fields; fractions elliptic ... See more keywords
On the Periodicity of Continued Fractions in Hyperelliptic Fields over Quadratic Constant Field
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DOI: 10.1134/s1064562418060091
Abstract: We give a description of the cubic polynomials f(x) with coefficients in the quadratic number fields $$\mathbb{Q}(\sqrt{5})$$Q(5) and $$\mathbb{Q}(\sqrt{-15})$$Q(−15) for which the continued fraction expansion of the irrationality $$\sqrt {f\left( x \right)} $$f(x) is periodic. read more here.
Keywords: hyperelliptic fields; periodicity continued; continued fractions; quadratic constant ... See more keywords
A note on approximation efficiency and partial quotients of Engel continued fractions
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DOI: 10.1142/s1793042117501329
Abstract: We consider the efficiency of approximating real numbers by their convergents of Engel continued fractions (ECF). Specifically, we estimate the Hausdorff dimension of the set of points whose ECF-co... read more here.
Keywords: approximation efficiency; continued fractions; efficiency partial; engel continued ... See more keywords