Journal of Integer Sequences, Vol. 16 (2013), Article 13.6.6

Dedekind Sums with Arguments near Certain Transcendental Numbers


Kurt Girstmair
Institut für Mathematik
Universität Innsbruck
Technikerstr. 13/7
A-6020 Innsbruck
Austria

Abstract:

We study the asymptotic behavior of the classical Dedekind sums s(sk/tk) for the sequence of convergents sk/tk $k\ge 0$, of the transcendental number

\begin{displaymath}\sum_{j=0}^\infty\frac 1{b^{2^j}},\ b\ge 3. \end{displaymath}

In particular, we show that there are infinitely many open intervals of constant length such that the sequence s(sk/tk) has infinitely many transcendental cluster points in each interval.

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Received April 9 2013; revised version received June 20 2013. Published in Journal of Integer Sequences, July 29 2013.

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