Journal of Integer Sequences, Vol. 23 (2020), Article 20.5.4

The Petersson-Knopp Identity and Farey Points

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


We study Dedekind sums S(a,b) for arguments a near Farey points of the interval [0, b]. The Petersson-Knopp identity connects each of these Dedekind sums with a set of other Dedekind sums. In the case considered here, this identity has a very specific interpretation, inasmuch as each Dedekind sum occurring in this identity is close to a certain expected value. Conversely, each of these expected values occurs with a certain frequency, a frequency that is consistent with the Petersson-Knopp identity.

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Received February 19 2020; revised version received May 17 2020. Published in Journal of Integer Sequences, May 17 2020.

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