Higher-power moments of Fourier coefficients of holomorphic cusp forms for the congruence subgroup Γ 0 ( N )

Let Sk(N) be the space of all holomorphic cusp forms of even integral weight k for the congruence group Γ0(N). For any f∈Sk(N) with ‖f‖2=1, we study the higher-power moments of ∑n≤xaf(n), where af(n) is the nth normalized Fourier coefficient of f. Furthermore, as an application, we investigate the h...

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Bibliographic Details
Published inThe Ramanujan journal Vol. 47; no. 3; pp. 685 - 700
Main Authors Zhang, Deyu, Wang, Yingnan
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.01.2018
Subjects
Coefficients
Mathematical analysis
Progressions
Subgroups
Weight
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Summary:Let Sk(N) be the space of all holomorphic cusp forms of even integral weight k for the congruence group Γ0(N). For any f∈Sk(N) with ‖f‖2=1, we study the higher-power moments of ∑n≤xaf(n), where af(n) is the nth normalized Fourier coefficient of f. Furthermore, as an application, we investigate the higher-power moments of Fourier coefficients in arithmetic progressions.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-018-0051-6