On certain kernel functions and shifted convolution sums of Hecke eigenvalues
| Autor: | Wang, Youjun |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\Gamma=SL(2,\mathbb{Z})$. Denote by $\lambda_{\text{sym}^{j}f}(n)$ 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 $\lambda_{\text{sym}^{j}f}(n)$ with a weight function to be the $k$-full kernel function for any fixed integer $k\geq 2$. Comment: 14 pages |
| Databáze: | arXiv |
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