2015/02/26 by Ian D. Morris, Morris, Ian D. · 1 citation
Engineering · Mathematics · #11K50 #37D35 #68W40 #Advanced Numerical Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Mathematical functions and polynomials #Number Theory (math.NT) #Primary 11A05 #Secondary 37D20
paper · pdf · doi:10.48550/arxiv.1502.07616
openalex publication_date 2015/02/26 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28
D. Hensley showed in 1994 that the number of steps taken by the Euclidean\nalgorithm to find the greatest common divisor of two natural numbers less than\nor equal to n follows a normal distribution in the limit as n tends to\ninfinity. V. Baladi and B. Vall 'ee subsequently gave an alternative proof for\nboth the classical Euclidean algorithm and several of its close variants, based\non a detailed investigation of spectral properties of the transfer operator\nassociated to the Gauss map, building on deep results of D. Dolgopyat. In this\narticle we give a much shorter, albeit less quantitative, proof of this result\nusing only basic spectral properties of the transfer operator together with the\nmethod of moments and a Tauberian theorem due to H. Delange.\n