$L^4$-norms of automorphic forms in the depth aspect
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917288304705536 |
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| author | Fischer, Marius |
| author_facet | Fischer, Marius |
| contents | Let $p$ be an odd prime, and suppose $f$ is an $L^2$-normalised newform for $Γ_0(p^n)$ with bounded spectral parameters and trivial central character. We prove the optimal $L^4$-norm bound $\lVert f \rVert_4 \ll_{p,\varepsilon}(p^{n})^\varepsilon $ for all $\varepsilon >0$ as $n \rightarrow \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L^4$-norms of automorphic forms in the depth aspect Fischer, Marius Number Theory Primary 11F41, Secondary 11F70, 11S80 Let $p$ be an odd prime, and suppose $f$ is an $L^2$-normalised newform for $Γ_0(p^n)$ with bounded spectral parameters and trivial central character. We prove the optimal $L^4$-norm bound $\lVert f \rVert_4 \ll_{p,\varepsilon}(p^{n})^\varepsilon $ for all $\varepsilon >0$ as $n \rightarrow \infty$. |
| title | $L^4$-norms of automorphic forms in the depth aspect |
| topic | Number Theory Primary 11F41, Secondary 11F70, 11S80 |
| url | https://arxiv.org/abs/2602.19646 |