Vol. 12, No. 7, 2018

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

Volume 14
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

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
Density theorems for exceptional eigenvalues for congruence subgroups

Peter Humphries

Vol. 12 (2018), No. 7, 1581–1610
Abstract

Using the Kuznetsov formula, we prove several density theorems for exceptional Hecke and Laplacian eigenvalues of Maaß cusp forms of weight 0 or 1 for the congruence subgroups Γ0(q), Γ1(q), and Γ(q). These improve and extend upon results of Sarnak and Huxley, who prove similar but slightly weaker results via the Selberg trace formula.

Keywords
Selberg eigenvalue conjecture, Ramanujan conjecture
Mathematical Subject Classification 2010
Primary: 11F72
Secondary: 11F30
Milestones
Received: 30 January 2017
Revised: 2 April 2018
Accepted: 2 June 2018
Published: 27 October 2018
Authors
Peter Humphries
Department of Mathematics
University College London
United Kingdom