This article is cited in 3 papers

On Gauss — Kuz'min statistics in short intervals

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: The article is devoted to investigation of Gauss — Kuz'min statistics for rational numbers $a/b$, where $b$ is fixed, $1\le a\le b$, $(a,b)=1$. New asymptotic formula for the mean value of Gauss — Kuz'min statistics is proved. It sharpens previous result which is similar to the Porter's theorem.

Key words: Euclidean algorithm, continued fractions, Kloosterman sums, Gauss — Kuz'min statistics.

UDC: 511.37, 511.336

MSC: Primary 11L05; Secondary 11Y16

Received: 01.11.2010