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arXiv · 1502.01006

Local bounds for $L^p$ norms of Maass forms in the level aspect

Simon Marshall
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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.

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Simon Marshall. 2015-02-03. Local bounds for $L^p$ norms of Maass forms in the level aspect. https://doi.org/10.2140/ant.2016.10.803

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