Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group Γ = SL (2, Z). Let λₒₘ₌₉ ₅ (n) denote the n-th normalized coefficients of the Dirichlet expansion of the j-th symmetric power L-function L (symj f, s). In this paper, we are interested in the average behaviour of the higher moments of λₒₘ₌₉ ₅ (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 λₒₘ₌₉ ₅ (n) for j ⩾ 3 in the interval (x, 2x].
Guodong Hua (Wed,) studied this question.