Results 11 to 20 of about 125,919 (262)
Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion
Advances in Difference Equations, 2019 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 great variety of ...
Hendrik Baumann
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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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Transcendental Continued Fractions
Communications in Mathematics, 2022 In the present paper, we give sufficient conditions on the elements of the continued fractions $A$ and $B$ that will assure us that the continued fraction $A^B$ is a transcendental number. With the same condition, we establish a transcendental measure of $A^B.$
Ahallal, Sarra, Kacha, Ali
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Location of approximations of a Markoff theorem
International Journal of Mathematics and Mathematical Sciences, 1990 Relative to the first two theorems of the well known Markoff Chain (J.W.S. Cassels, An introduction to diophantine approximation approximations are well located.
K. C. Prasad, M. Lari, P. Singh
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The Reciprocal of a Continued Fraction [PDF]
Proceedings of the American Mathematical Society, 1952 Stieltjes [3, Chapter X],1 and later Rogers [2], gave formulas by means of which the reciprocal continued fractions for continued fractions of a certain class may be determined. We give below a theorem which extends the class of continued fractions to which this reciprocal transformation is applicable ;2 moreover, the theorem is stated in terms of ...
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On generalization of continued fraction of Gauss
International Journal of Mathematics and Mathematical Sciences, 1990 In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
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The discrete logarithm problem modulo one: cryptanalysing the Ariffin–Abu cryptosystem
Journal of Mathematical Cryptology, 2010 The paper provides a cryptanalysis of the AAβ-cryptosystem recently proposed by Ariffin and Abu. The scheme is in essence a key agreement scheme whose security is based on a discrete logarithm problem in the infinite (additive) group ℝ/ℤ (the reals ...
Blackburn Simon R.
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Continued fractions and class number two
International Journal of Mathematics and Mathematical Sciences, 2001 We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm-induced quadratic polynomial.
Richard A. Mollin
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$q$-DEFORMED RATIONALS AND $q$-CONTINUED FRACTIONS
Forum of Mathematics, Sigma, 2020 We introduce a notion of $q$-deformed rational numbers and $q$-deformed continued fractions. A $q$-deformed rational is encoded by a triangulation of a polygon and can be computed recursively. The recursive formula is analogous to the $q$-deformed Pascal
SOPHIE MORIER-GENOUD, VALENTIN OVSIENKO
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Polynomial continued fractions [PDF]
Acta Arithmetica, 2002 Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one.
Bowman, Douglas, McLaughlin, James
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