Uniform estimates for sums of coefficients of symmetric square L-function

Let ϕ(z)ϕ(z) denote a holomorphic or Maass cusp form for the full modular group Γ=SL(2,Z)Γ=SL(2,Z). And let λSym2ϕ(n) be the n-th coefficient of symmetric square L  -function associated with ϕ(z)ϕ(z). We establish the uniform upper bound for the summatory function∑n≤xλSym2ϕ(n), which improves the results of Ichihara [4], Lü [10], Sankaranarayanan [13] and Tang [14].