The sup-norm problem for newforms of large level on $\operatorname{PGL}(n)$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917258174922752 |
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| author | Toma, Radu |
| author_facet | Toma, Radu |
| contents | Let $N$ be a prime and $ϕ$ be a Hecke-Maass cuspidal newform for the Hecke congruence subgroup $Γ_0(N)$ in $\operatorname{SL}_n(\mathbb{R})$. Let $Ω$ be an adelic compactum and let $Ω_N$ be its projection to $Γ_0(N) \backslash \operatorname{SL}_n(\mathbb{R}) / \operatorname{SO}(n)$. For any prime $n$, we prove sub-baseline bounds for the sup-norm of $ϕ$ restricted to $Ω_N$. Conditionally on GRH, we generalise this result to all $n \geq 2$. The methods involve a new reduction theory with level structure, based on generalisations of Atkin-Lehner operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02741 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The sup-norm problem for newforms of large level on $\operatorname{PGL}(n)$ Toma, Radu Number Theory 11F12 (Primary) 11F72, 11D45, 11F06, 11H55, 11H06 (Secondary) Let $N$ be a prime and $ϕ$ be a Hecke-Maass cuspidal newform for the Hecke congruence subgroup $Γ_0(N)$ in $\operatorname{SL}_n(\mathbb{R})$. Let $Ω$ be an adelic compactum and let $Ω_N$ be its projection to $Γ_0(N) \backslash \operatorname{SL}_n(\mathbb{R}) / \operatorname{SO}(n)$. For any prime $n$, we prove sub-baseline bounds for the sup-norm of $ϕ$ restricted to $Ω_N$. Conditionally on GRH, we generalise this result to all $n \geq 2$. The methods involve a new reduction theory with level structure, based on generalisations of Atkin-Lehner operators. |
| title | The sup-norm problem for newforms of large level on $\operatorname{PGL}(n)$ |
| topic | Number Theory 11F12 (Primary) 11F72, 11D45, 11F06, 11H55, 11H06 (Secondary) |
| url | https://arxiv.org/abs/2401.02741 |