Euclidean algorithms are Gaussian

DOI10.1016/j.jnt.2004.08.008zbMath1114.11092OpenAlexW2056364851MaRDI QIDQ1771021

Viviane Baladi, Brigitte Vallée

Publication date: 7 April 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.08.008

zbMATH Keywords

Dynamical systemsDirichlet seriesPerron's formulaCentral limit theoremTransfer operatorLocal limit theoremProbabilistic analysis of algorithms

Mathematics Subject Classification ID

Related Items (40)

Modularity and value distribution of quantum invariants of hyperbolic knots ⋮ Explicit spectral gaps for random covers of Riemann surfaces ⋮ A note on ``Euclidean algorithms are Gaussian by V. Baladi and B. Vallée ⋮ Statistical properties of finite continued fractions with fixed denominator ⋮ Hyperbolic systems, zeta functions and other friends ⋮ Exponential decay of correlations for surface semi-flows without finite Markov partitions ⋮ Limit theorems for fast-slow partially hyperbolic systems ⋮ The Brun gcd algorithm in high dimensions is almost always subtractive ⋮ Slow continued fractions, transducers, and the Serret theorem ⋮ Dynamics of Ostrowski skew-product: 1. Limit laws and Hausdorff dimensions ⋮ Large degree covers and sharp resonances of hyperbolic surfaces ⋮ Limit laws for rational continued fractions and value distribution of quantum modular forms ⋮ Statistical distribution of the Stern sequence ⋮ Bias in the number of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums ⋮ Numeration and discrete dynamical systems ⋮ Probabilistic analyses of the plain multiple gcd algorithm ⋮ On the distribution of partial quotients of reduced fractions with fixed denominator ⋮ Small quotients in Euclidean algorithms ⋮ Gaussian Distribution of Trie Depth for Strongly Tame Sources ⋮ 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 ⋮ The dynamics of Pythagorean Triples ⋮ The mean number of steps in the Euclidean algorithm with odd partial quotients ⋮ Density and location of resonances for convex co-compact hyperbolic surfaces ⋮ Exponential Mixing: Lectures from Mumbai ⋮ What do continued fractions accomplish? ⋮ High moments of the Estermann function ⋮ Estimate for dispersion of lengths of continued fractions ⋮ On Gauss-Kuz'min statistics for finite continued fractions ⋮ Expanding maps on Cantor sets and analytic continuation of zeta functions ⋮ Gaussian laws for the main parameters of the Euclid algorithms ⋮ Analysis of generalized continued fraction algorithms over polynomials ⋮ A local limit theorem with speed of convergence for Euclidean algorithms and Diophantine costs ⋮ Decreasing height along continued fractions ⋮ Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences ⋮ Regularity of the Euclid algorithm; application to the analysis of fast GCD algorithms ⋮ The mean number of steps in the Euclidean algorithm with least absolute value remainders ⋮ Distribution of periodic points of certain Gauss shifts with infinite invariant measure ⋮ Gaussian behavior of quadratic irrationals ⋮ Comparison theorems for closed geodesics on negatively curved surfaces

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