Far Eastern Mathematical Journal

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On Gauss — Kuz'min statistics in short intervals

A. V. Ustinov

2011, issue 1, P. 93–98

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.

Keywords:
Euclidean algorithm, continued fractions, Kloosterman sums, Gauss — Kuz'min statistics

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