On the higher power moments of Dirichlet coefficients of symmetric power L-functions and its applications

Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group Γ = SL(2,Z). Let {λsymj f} (n) denote the n-th normalized coefficients of the Dirichlet expansion of the j-th symmetric power L-function L( sym{j} f, s). In this paper, we are interested in the average behaviour of the higher moments of {λsymj f} (n) for j ⩾ 2, which refines the previous results in this direction. As an application, we also consider the number of sign changes of the sequence { {λsymj f} (n)} for j ⩾ 3 in the interval (x, 2x].