On certain kernel functions and shifted convolution sums of Hecke eigenvalues
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910405901680640 |
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| author | Wang, Youjun |
| author_facet | Wang, Youjun |
| contents | Let $j\geq 2$ be a given integer. Let $f$ be a normalized primitive holomorphic cusp form of even integral weight for the full modular group $Γ=SL(2,\mathbb{Z})$. Denote by $λ_{\text{sym}^{j}f}(n)$ the $n$th normalized coefficient of the Dirichlet expansion of the $j$th symmetric power $L$-function $L(s,\text{sym}^{j}f)$. In this paper, we are interested in the behavior of the shifted convolution sum involving $λ_{\text{sym}^{j}f}(n)$ with a weight function to be the $k$-full kernel function for any fixed integer $k\geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On certain kernel functions and shifted convolution sums of Hecke eigenvalues Wang, Youjun Number Theory 11F11 (Primary) 11F30, 11F66 (Secondary) Let $j\geq 2$ be a given integer. Let $f$ be a normalized primitive holomorphic cusp form of even integral weight for the full modular group $Γ=SL(2,\mathbb{Z})$. Denote by $λ_{\text{sym}^{j}f}(n)$ the $n$th normalized coefficient of the Dirichlet expansion of the $j$th symmetric power $L$-function $L(s,\text{sym}^{j}f)$. In this paper, we are interested in the behavior of the shifted convolution sum involving $λ_{\text{sym}^{j}f}(n)$ with a weight function to be the $k$-full kernel function for any fixed integer $k\geq 2$. |
| title | On certain kernel functions and shifted convolution sums of Hecke eigenvalues |
| topic | Number Theory 11F11 (Primary) 11F30, 11F66 (Secondary) |
| url | https://arxiv.org/abs/2404.05313 |