Euclidean algorithm中除法步数服从正态分布的一个简短证明
A short proof that the number of division steps in the Euclidean algorithm is normally distributed
摘要：
D.汉斯莱在1994年表明，采取的步骤数欧几里德算法找到最大公因数的两个自然数小于或等于n遵循正态分布的限制，因为n趋于无穷大。V.Baladi和B. Vallée随后给出了一个替代证明的经典欧几里德算法和它的几个密切的变种，基于一个详细的调查的频谱性质的转移算子相关的高斯映射，建立在深入的结果D。多尔戈皮亚特在这篇文章中，我们给出了一个更短的，虽然不太定量，证明这个结果只使用基本的谱性质的转移算子的矩量法和Tauberian定理由于H。德朗热
英文摘要：
D. Hensley showed in 1994 that the number of steps taken by the Euclidean algorithm to find the greatest common divisor of two natural numbers less than or equal to n follows a normal distribution in the limit as n tends to infinity. V. Baladi and B. Vallée subsequently gave an alternative proof for both the classical Euclidean algorithm and several of its close variants, based on a detailed investigation of spectral properties of the transfer operator associated to the Gauss map, building on deep results of D. Dolgopyat. In this article we give a much shorter, albeit less quantitative, proof of this result using only basic spectral properties of the transfer operator together with the method of moments and a Tauberian theorem due to H. Delange.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
