Vol. 10, No. 4, 2016

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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