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
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
On the automaticity of sequences defined by the Thue–Morse and period-doubling Stieltjes continued fractions
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DOI: 10.1142/s1793042120501134
Abstract: Continued fraction expansions of automatic numbers have been extensively studied during the last few decades. The research interests are, on one hand, in the degree or automaticity of the partial quotients following the seminal paper… read more here.
Keywords: thue morse; continued fractions; defined thue; stieltjes continued ... See more keywords
Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion
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DOI: 10.1186/s13662-019-2340-9
Abstract: In the literature, many generalizations of continued fractions have been introduced, and for each of them, convergence results have been proved. In this paper, we suggest a definition of generalized continued fractions which covers a… read more here.
Keywords: pringsheim type; definition; continued fractions; type convergence ... See more keywords
Approximation for the Ratios of the Confluent Hypergeometric Function ΦD(N) by the Branched Continued Fractions
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DOI: 10.3390/axioms11090426
Abstract: The paper deals with the problem of expansion of the ratios of the confluent hypergeometric function of N variables ΦD(N)(a,b¯;c;z¯) into the branched continued fractions (BCF) of the general form with N branches of branching… read more here.
Keywords: ratios confluent; function; continued fractions; confluent hypergeometric ... See more keywords