The Petersson-Knopp Identity and Farey Points
Institut für Mathematik
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
Full version: pdf,
Received February 19 2020;
revised version received May 17 2020.
Published in Journal of Integer Sequences,
May 17 2020.
Journal of Integer Sequences home page