English

The Petersson-Knopp identity and Farey neighbours

Number Theory 2019-04-02 v1

Abstract

We study Dedekind sums S(a,b)S(a,b) near Farey points of the interval [0,b][0,b]. 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.

Keywords

Cite

@article{arxiv.1904.00873,
  title  = {The Petersson-Knopp identity and Farey neighbours},
  author = {Kurt Girstmair},
  journal= {arXiv preprint arXiv:1904.00873},
  year   = {2019}
}