Abstract
We study the behaviour of the classical Dedekind sums s ( m / n ) for convergents m / n of a given quadratic irrational α . It turns out that two cases may occur: Either the sequence s ( m / n ) remains bounded with finitely many cluster points, or s ( m / n ) tends to +∞ or −∞ like + log n or − log n , respectively. By means of the Barkan–Hickerson–Knuth formula we obtain a precise description of what happens in all cases.
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