Vol. 12, No. 3, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Mean square in the prime geodesic theorem

Giacomo Cherubini and João Guerreiro

Vol. 12 (2018), No. 3, 571–597
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.

Keywords
prime geodesic theorem, Selberg trace formula, Kuznetsov trace formula, Kloosterman sums
Mathematical Subject Classification 2010
Primary: 11F72
Secondary: 11L05, 11M36
Milestones
Received: 23 May 2017
Revised: 26 October 2017
Accepted: 30 December 2017
Published: 12 June 2018
Authors
Giacomo Cherubini
Max-Planck-Institut für Mathematik
Bonn
Germany
João Guerreiro
Max-Planck-Institut für Mathematik
Bonn
Germany