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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.12465 |
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| _version_ | 1866909915340079104 |
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| author | Sun, Qingfeng Zhang, Qizhi |
| author_facet | Sun, Qingfeng Zhang, Qizhi |
| contents | We find some equidistribution results connected to restriction quantum unique ergodicity problem in this paper. We shows that \begin{align*}
\frac{1}{|\mathcal{B}_k|}\sum_{f\in \mathcal{B}_k} \int_{R}y^{k}|f(z)|^{2}ψ(z) dμ_{R}(z)\to \frac{3}π\int_{R}ψ(z) dμ_{R}(z) \end{align*} where $R$ is some subset of $\mathbb{H}$, $ψ$ is a nice function relative to $R$, $dμ_{R}(z)$ is a suitable measure on $R$, and $\mathcal{B}_k$ is an orthonormal basis of the cusp forms for group $Γ$ with respect to weight $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12465 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equidistribution of holomorphic cusp forms on thin sets Sun, Qingfeng Zhang, Qizhi Number Theory We find some equidistribution results connected to restriction quantum unique ergodicity problem in this paper. We shows that \begin{align*} \frac{1}{|\mathcal{B}_k|}\sum_{f\in \mathcal{B}_k} \int_{R}y^{k}|f(z)|^{2}ψ(z) dμ_{R}(z)\to \frac{3}π\int_{R}ψ(z) dμ_{R}(z) \end{align*} where $R$ is some subset of $\mathbb{H}$, $ψ$ is a nice function relative to $R$, $dμ_{R}(z)$ is a suitable measure on $R$, and $\mathcal{B}_k$ is an orthonormal basis of the cusp forms for group $Γ$ with respect to weight $k$. |
| title | Equidistribution of holomorphic cusp forms on thin sets |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.12465 |