$L^4$-norms of automorphic forms in the depth aspect
Abstract
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 $n \rightarrow \infty$.
Fields of Study & Subjects
Advanced Algebra and Geometry
Analytic Number Theory Research
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 23 February 2026
- Language
- EN
- Document type
- Preprint