Estimates for Fourier Coefficients of Cusp Forms in Weight Aspect

Estimates for Fourier Coefficients of Cusp Forms in Weight Aspect

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摘要 Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(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 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.

作者 Hengcai TANG

机构地区 Department of Mathematics

出处《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第5期793-802,共10页 数学年刊（B辑英文版）

基金 supported by the National Natural Science Foundation of China(No.11301142) the Key Project of Colleges and Universities of Henan Province(No.15A110014)

关键词 Forms normalized symmetric modular absolute instead Mellin inequality sufficiently approximate Fourier 系数；尖顶形式；对称的方形的 L 功能；

分类号 O174.21 [理学—基础数学]

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Chinese Annals of Mathematics,Series B

2016年第5期

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Estimates for Fourier Coefficients of Cusp Forms in Weight Aspect

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