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| Estimates for Fourier Coefficients of Cusp Forms in Weight Aspect |
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Citation： |
Hengcai TANG.Estimates for Fourier Coefficients of Cusp Forms in Weight Aspect[J].Chinese Annals of Mathematics B,2016,37(5):793~802 |
| Page view： 1311
Net amount： 1138 |
Authors： |
Hengcai TANG; |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11301142) and the Key Project of Colleges
and Universities of Henan Province (No.15A110014). |
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| Abstract： |
Let $f$ be a holomorphic Hecke eigenform of weight $k$ for the modular group
$\Gamma=SL_2(\mathbb{Z})$ and let $\lambda_f(n)$ be the $n$-th normalized Fourier coefficient.
In this paper, by a new estimate of the second integral moment of the symmetric square
$L$-function related to $f$, the estimate
$$
\sum_{n\leq x}\lambda_f(n^2) \ll x^{\frac{1}{2}}k^{\frac{1}{2}}(\log
(x+k))^6
$$
is established, which improves the previous result. |
Keywords： |
Fourier coefficients, Cusp forms, Symmetric square $L$-function |
Classification： |
11F30, 11F11, 11F66 |
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