The number of steps in the Euclidean algorithm
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Publication:5906618
DOI10.1006/jnth.1994.1088zbMath0811.11055OpenAlexW2065660572MaRDI QIDQ5906618
Publication date: 11 December 1994
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jnth.1994.1088
Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)
Related Items (20)
New normality constructions for continued fraction expansions ⋮ A note on ``Euclidean algorithms are Gaussian by V. Baladi and B. Vallée ⋮ Obfuscated fuzzy Hamming distance and conjunctions from subset product problems ⋮ Continued fraction algorithms, functional operators, and structure constants ⋮ The rate of convergence of approximations of a continued fraction ⋮ Statistical distribution of the Stern sequence ⋮ Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums ⋮ Dynamical analysis of a class of Euclidean algorithms. ⋮ Probabilistic analyses of the plain multiple gcd algorithm ⋮ A rigorous version of R. P. Brent's model for the binary Euclidean algorithm ⋮ Fine costs for Euclid's algorithm on polynomials and Farey maps ⋮ Another note on “Euclidean algorithms are Gaussian” by V. Baladi and B. Vallée ⋮ High moments of the Estermann function ⋮ Estimate for dispersion of lengths of continued fractions ⋮ On Gauss-Kuz'min statistics for finite continued fractions ⋮ Gaussian laws for the main parameters of the Euclid algorithms ⋮ Digits and continuants in Euclidean algorithms. Ergodic versus Tauberian theorems ⋮ Euclidean algorithms are Gaussian ⋮ A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs ⋮ Regularity of the Euclid algorithm; application to the analysis of fast GCD algorithms
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