Vol. 10, No. 4, 2016

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

Volume 12, 1 issue

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
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Local bounds for $L^p$ norms of Maass forms in the level aspect

Simon Marshall

Vol. 10 (2016), No. 4, 803–812
DOI: 10.2140/ant.2016.10.803

We apply techniques from harmonic analysis to study the Lp norms of Maass forms of varying level on a quaternion division algebra. Our first result gives a candidate for the local bound for the sup norm in terms of the level, which is new when the level is not squarefree. The second result is a bound for Lp norms in the level aspect that is analogous to Sogge’s theorem on Lp norms of Laplace eigenfunctions.

$L^p$ norms, sup norms, Maass forms, automorphic forms
Mathematical Subject Classification 2010
Primary: 35P20
Secondary: 11F41, 11F25
Received: 9 March 2015
Revised: 31 December 2015
Accepted: 23 April 2016
Published: 20 June 2016
Simon Marshall
Department of Mathematics
University of Wisconsin-Madison
480 Lincoln Drive
Madison, WI 53706
United States