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arXiv · 2512.03482

Kakeya-Nikodym norms of Maass forms on $\rm{U}(2,1)$

Jiaqi Hou
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Abstract

Let $\psi$ be a Hecke-Maass form with a large spectral parameter on a compact arithmetic complex hyperbolic surface. We apply the amplification method to obtain a power saving over the trivial bound for the Kakeya-Nikodym norm of $\psi$. As a consequence, we obtain power savings over the local bound of Sogge for $\|\psi\|_p$ when $2<p<10/3$.

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Jiaqi Hou. 2025-12-03. Kakeya-Nikodym norms of Maass forms on $\rm{U}(2,1)$. https://arxiv.org/abs/2512.03482

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