【摘 要】
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Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full modular group.Let λf(n) be the nth normalized Fourier coefficient of f(z).Suppose that L
【机 构】
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School of Mathematical Sciences
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Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full modular group.Let λf(n) be the nth normalized Fourier coefficient of f(z).Suppose that L(sym2f,s) is the symmetric square L-function associated with f(z),and λsym2f(n) denotes the nth coefficient L(sym2f,s).In this paper,it is proved that Σn≤x λ4sym2f(n) =xP2(logx) + O(x79/81 +ε ),where P2(t) is a polynomial in t of degree 2.Similarly,it is obtained that 79 ~Σn≤x λ4f(n2) =x(P)2(logx) + O(x79/81+ε ),where (P)2(t) is a polynomial in t of degree 2.
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