On $\rm GL_3$ Fourier coefficients over values of mixed powers
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913774953299968 |
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| author | Yu, Yanxue |
| author_facet | Yu, Yanxue |
| contents | Let $A_π(n,1)$ be the $(n,1)$-th Fourier coefficient of the Hecke-Maass cusp form $π$ for $\rm SL_3(\mathbb{Z})$ and $ ω(x)$ be a smooth compactly supported function. In this paper, we prove a nontrivial upper bound for the sum $$\sum_{n_1,\cdots,n_\ell,n_{\ell+1}\in\mathbb{Z}^+ \atop n=n_1^r+\cdots+n_{\ell}^r+n_{\ell+1}^s} A_π(n,1)ω\left(n/X\right),$$ where $r\geq2$, $s\geq 2$ and $\ell\geq 2^{r-1}$ are integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02315 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $\rm GL_3$ Fourier coefficients over values of mixed powers Yu, Yanxue Number Theory 11P05, 11F30 Let $A_π(n,1)$ be the $(n,1)$-th Fourier coefficient of the Hecke-Maass cusp form $π$ for $\rm SL_3(\mathbb{Z})$ and $ ω(x)$ be a smooth compactly supported function. In this paper, we prove a nontrivial upper bound for the sum $$\sum_{n_1,\cdots,n_\ell,n_{\ell+1}\in\mathbb{Z}^+ \atop n=n_1^r+\cdots+n_{\ell}^r+n_{\ell+1}^s} A_π(n,1)ω\left(n/X\right),$$ where $r\geq2$, $s\geq 2$ and $\ell\geq 2^{r-1}$ are integers. |
| title | On $\rm GL_3$ Fourier coefficients over values of mixed powers |
| topic | Number Theory 11P05, 11F30 |
| url | https://arxiv.org/abs/2504.02315 |