Abstract
We apply techniques from harmonic analysis to study the 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 norms in the level aspect that is analogous to Sogge’s theorem on norms of Laplace eigenfunctions.
Citation
Simon Marshall. "Local bounds for $L^p$ norms of Maass forms in the level aspect." Algebra Number Theory 10 (4) 803 - 812, 2016. https://doi.org/10.2140/ant.2016.10.803
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