The law of large numbers for the sum of the partial quotients of a rational number with fixed denominator

被引：0

作者：

M. G. Rukavishnikova

机构：

[1] Far-Eastern Branch of the Russian Academy of Sciences,Far

来源：

Mathematical Notes | 2011年 / 90卷

关键词：

law of large numbers; rational number; continued fraction; partial quotient; Euler function; Möbius function; Riemann zeta function;

D O I：

暂无

中图分类号：

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摘要：

We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients.

引用

共 5 条

[1]

Yao A. C.(1975)Analysis of the subtractive algorithm for greatest common divisors Proc. Nat. Acad. Sci.U. S. A. 72 4720-4722

[2]

Knuth D. E.(1982)The mean for a sum of elements in a class of finite continued fractions Mat. Zametki 32 593-600

[3]

Panov A. A.(2006)A probability estimate for the sum of incomplete partial quotients with fixed denominator Chebyshevskii Sb. 7 113-121

[4]

Rukavishnikova M. G.(2005)Estimate for dispersion of lengths of continued fractions Fundam. Prikl.Mat. 11 15-26

[5]

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