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arXiv · 2602.19646

$L^4$-norms of automorphic forms in the depth aspect

Marius Fischer
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Abstract

Let $p$ be an odd prime, and suppose $f$ is an $L^2$-normalised newform for $\Gamma_0(p^n)$ 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 $n \rightarrow \infty$.

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Marius Fischer. 2026-02-23. $L^4$-norms of automorphic forms in the depth aspect. https://arxiv.org/abs/2602.19646

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