Article
| Title: | On higher moments of Hecke eigenvalues attached to cusp forms (English) |
| Author: | Hua, Guodong |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 1055-1064 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $f$, $g$ and $h$ be three distinct primitive holomorphic cusp forms of even integral weights $k_{1}$, $k_{2}$ and $k_{3}$ for the full modular group $\Gamma ={\rm SL}(2,\mathbb {Z})$, respectively, and let $\lambda _{f}(n)$, $\lambda _{g}(n)$ and $\lambda _{h}(n)$ denote the $n$th normalized Fourier coefficients of $f$, $g$ and $h$, respectively. We consider the cancellations of sums related to arithmetic functions $\lambda _{g}(n)$, $\lambda _{h}(n)$ twisted by $\lambda _{f}(n)$ and establish the following results: $$ \sum _{n\leq x}\lambda _{f}(n)\lambda _{g}(n)^{i}\lambda _{h}(n)^{j} \ll _{f,g,h,\varepsilon } x^{1- 1/2^{i+j} +\varepsilon } $$ for any $\varepsilon >0$, where $1\leq i\leq 2$, $j\geq 5$ are any fixed positive integers. (English) |
| Keyword: | Hecke eigenform |
| Keyword: | Fourier coefficient |
| Keyword: | Rankin-Selberg $L$-function |
| MSC: | 11F11 |
| MSC: | 11F30 |
| MSC: | 11F66 |
| idZBL: | Zbl 07655782 |
| idMR: | MR4517595 |
| DOI: | 10.21136/CMJ.2022.0330-21 |
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| Date available: | 2022-11-28T11:36:57Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151129 |
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