摘要
Let a(n) be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A(x) =∑n≤xa(n).In this paper, we establish an asymptotic formula of tile fourth power moment of A(x) and prove that ∫1^TA^4(x)dx=3/64κπ^4s4;2(a^~)T^2κ+O(T^2a-δ4+t) with δ4 = 1/8, which improves the previous result.
Let a(n) be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A(x) =∑n≤xa(n).In this paper, we establish an asymptotic formula of tile fourth power moment of A(x) and prove that ∫1^TA^4(x)dx=3/64κπ^4s4;2(a^~)T^2κ+O(T^2a-δ4+t) with δ4 = 1/8, which improves the previous result.