This article is cited in 6 papers

The average length of reduced regular continued fractions

E. N. Zhabitskaya

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Let $l(a/b)$ be the number of steps of the by-excess Euclidean algorithm applied to the numbers $a$ and $b$. In this paper we obtain a three-term asymptotic formula for the expectation of the random value $l(a/b)$, when $1\le a\le b\le R$ and $R\to\infty$.
Bibliography: 11 titles.

Keywords: Euclidean algorithm, division by-excess, average length, continued fraction.

UDC: 511.335

MSC: Primary 11A55; Secondary 11K50

Received: 21.05.2008 and 27.03.2009

DOI: 10.4213/sm6367

 English version: Sbornik: Mathematics, 2009, 200:8, 1181–1214

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