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

• Published in: The Ramanujan journal Vol. 47; no. 3; pp. 685 - 700
• Main Authors: Zhang, Deyu, Wang, Yingnan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.01.2018
• Subjects: Coefficients; Mathematical analysis; Progressions; Subgroups; Weight

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...