Mean square in the prime geodesic theorem
Number Theory
2018-10-02 v2
Abstract
We prove upper bounds for the mean square of the remainder in the prime geodesic theorem, for every cofinite Fuchsian group, which improve on average on the best known pointwise bounds. The proof relies on the Selberg trace formula. For the modular group we prove a refined upper bound by using the Kuznetsov trace formula.
Cite
@article{arxiv.1702.00297,
title = {Mean square in the prime geodesic theorem},
author = {Giacomo Cherubini and João Guerreiro},
journal= {arXiv preprint arXiv:1702.00297},
year = {2018}
}
Comments
23 pages, corrected a few typos and inaccuracies