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The Petersson-Knopp Identity and Farey Points
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Kurt Girstmair

Institut für Mathematik

Universität Innsbruck

Technikerstr. 13/7

A-6020 Innsbruck

Austria

**Abstract:**

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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