The Petersson-Knopp identity and Farey neighbours
Number Theory
2019-04-02 v1
Abstract
We study Dedekind sums near Farey points of the interval . Each of these Dedekind sums is connected with a set of other Dedekind sums by the Petersson-Knopp identity. In the case considered here, this identity has a very specific interpretation, inasmuch as each Dedekind 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.
Cite
@article{arxiv.1904.00873,
title = {The Petersson-Knopp identity and Farey neighbours},
author = {Kurt Girstmair},
journal= {arXiv preprint arXiv:1904.00873},
year = {2019}
}