Kakeya-Nikodym norms of Maass forms on $\rm{U}(2,1)$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915651013050368 |
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| author | Hou, Jiaqi |
| author_facet | Hou, Jiaqi |
| contents | Let $ψ$ 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 $ψ$. As a consequence, we obtain power savings over the local bound of Sogge for $\|ψ\|_p$ when $2<p<10/3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kakeya-Nikodym norms of Maass forms on $\rm{U}(2,1)$ Hou, Jiaqi Number Theory Analysis of PDEs 58J50, 11F03 Let $ψ$ 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 $ψ$. As a consequence, we obtain power savings over the local bound of Sogge for $\|ψ\|_p$ when $2<p<10/3$. |
| title | Kakeya-Nikodym norms of Maass forms on $\rm{U}(2,1)$ |
| topic | Number Theory Analysis of PDEs 58J50, 11F03 |
| url | https://arxiv.org/abs/2512.03482 |