| Autor: |
Ilya Khayutin, Paul D. Nelson, Raphael S. Steiner |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
Forum of Mathematics, Pi, Vol 12 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2050-5086 |
| DOI: |
10.1017/fmp.2024.9 |
| Popis: |
Let f be an $L^2$ -normalized holomorphic newform of weight k on $\Gamma _0(N) \backslash \mathbb {H}$ with N squarefree or, more generally, on any hyperbolic surface $\Gamma \backslash \mathbb {H}$ attached to an Eichler order of squarefree level in an indefinite quaternion algebra over $\mathbb {Q}$ . Denote by V the hyperbolic volume of said surface. We prove the sup-norm estimate $$\begin{align*}\| \Im(\cdot)^{\frac{k}{2}} f \|_{\infty} \ll_{\varepsilon} (k V)^{\frac{1}{4}+\varepsilon} \end{align*}$$ |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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