Far Eastern Mathematical Journal

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The average length of Minkowski's diagonal continued fractions

O. A. Gorkusha

2011, issue 1, P. 10–27

We prove asymptotic formulae with two significant terms for the expectation of the random variable $s(c/d;1)$ — length of Minkowski's diagonal continued fraction when the variables $c$ and $d$ range over the set $1 \le c \le d \le R<\infty$.

Continued fractions, geometry of numbers, lattices

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