On Kuznetsov-Bykovskii's formula of counting prime geodesics
Number Theory
2022-06-22 v4
Abstract
We generalize a formula on the counting of prime geodesics, due to Kuznetsov-Bykovskii, used in the work of Soundararajan-Young on the prime geodesic theorem. The method works over any number field and for any congruence subgroup. We give explicit computation in the cases of principal and Hecke subgroups.
Cite
@article{arxiv.1901.03824,
title = {On Kuznetsov-Bykovskii's formula of counting prime geodesics},
author = {Giacomo Cherubini and Han Wu and Gergely Zábrádi},
journal= {arXiv preprint arXiv:1901.03824},
year = {2022}
}
Comments
Thm. 1.9 (PGT for congruence subgroups of $\operatorname{SL}_2(\mathbb{Z}[i])$) is new