Results 31 to 40 of about 5,022,265 (207)
On the dimension spectrum of infinite subsystems of continued fractions [PDF]
Transactions of the American Mathematical Society, 2018 In this paper we study the dimension spectrum of continued fractions with coefficients restricted to infinite subsets of natural numbers. We prove that if E E is any arithmetic progression, the set of primes, or the set of squares
Vasileios Chousionis +2 more
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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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Continued fractions and orderings on the Markov numbers [PDF]
, 2018 Markov numbers are integers that appear in the solution triples of the Diophantine equation, $x^2+y^2+z^2=3xyz$, called the Markov equation. A classical topic in number theory, these numbers are related to many areas of mathematics such as combinatorics,
Michelle Rabideau, R. Schiffler
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Ramanujan and the Regular Continued Fraction Expansion of Real Numbers [PDF]
, 2004 In some recent papers, the authors considered regular continued fractions of the form \[ [a_{0};\underbrace{a,...,a}_{m}, \underbrace{a^{2},...,a^{2}}_{m}, \underbrace{a^{3},...,a^{3}}_{m}, ...
Laughlin, James Mc, Wyshinski, Nancy J.
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Formulas for the Number of Spanning Trees in a Chain of Cycles
Sultan Qaboos University Journal for Science, 2010 We give a formula for the number of spanning trees in a chain of cycles that have connected intersection of one edge but where the cycles have variable sizes. The formula uses basic properties of continued fractions.
Thomas Bier
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Excursions of diffusion processes and continued fractions [PDF]
, 2010 It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process.
Comtet, Alain, Tourigny, Yves
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On structure of branched continued fractions
Carpathian Mathematical PublicationsThe paper provides a survey of various multidimensional generalizations of continued fractions that arose when solving the problem of approximating functions of one or several variables, including some hypergeometric functions. It is shown that all these
T. Antonova
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Cluster algebras and continued fractions [PDF]
Compositio Mathematica, 2016 We establish a combinatorial realization of continued fractions as quotients of cardinalities of sets. These sets are sets of perfect matchings of certain graphs, the snake graphs, that appear naturally in the theory of cluster algebras.
Ilke Çanakçi, R. Schiffler
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