科研之友
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摘要
We study the behaviour of the classical Dedekind sums s(m/n) for convergents m/n of a given quadratic irrational alpha. 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 +infinity or -infinity 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.
- 出版日期2012-8
