Vol. 10, No. 4, 2016

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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 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.

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