#### Vol. 10, No. 4, 2016

 Download this article For screen For printing
 Recent Issues
 The Journal Cover Editorial Board Editors' Addresses Editors' Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Subscriptions Editorial Login Contacts 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
##### Abstract

We apply techniques from harmonic analysis to study the ${L}^{p}$ 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 ${L}^{p}$ norms in the level aspect that is analogous to Sogge’s theorem on ${L}^{p}$ norms of Laplace eigenfunctions.

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