Results 21 to 30 of about 1,237,080 (283)
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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A geometric generalization of continued fractions for imaginary quadratic fields [PDF]
, 2021 The Euclidean Algorithm for the integers is well known and yields a finite continued fraction expansion for each rational number. Geometrically, successive convergents in this expansion correspond to endpoints of edges in the Farey tessellation of the ...
Scheckelhoff, Kristen +1 more
core
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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A Theorem on Continued Fractions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1959 One of the outstanding theorems in the theory of continued fractions is the result described by O. Perron, Die Lehre von den Kettenbrüchen (1912, 1929, 1954–7) as the transformation of Bauer and Muir (for brevity I shall call it the BM theorem); this theorem and limiting cases of it give rise to numerous extremely interesting consequences.
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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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A CONTINUED FRACTION TITBIT [PDF]
Fractals, 1995 In 1812 Gauss, in a letter to Laplace, proposed without proof a formula explaining the statistical regularity of continued fractions. There has since been speculation concerning the manner in which Gauss arrived at this formula. In this article we present a plausible explanation, which at the same time gives an elementary proof of the full ergodic ...
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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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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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