Mean value of Dirichlet series coefficients of Rankin–Selberg L-functions

Abstract Let π and π′ be irreducible cuspidal automorphic representations of GL m (?ℚ) and GL m′ (?ℚ), respectively. Denote by a π×π′ (n) the nth coefficient of the Dirichlet series of the Rankin–Selberg L-function associated with π and π′. In this paper, we obtain the upper bound for the sum Σ n ≤ x a π × π'(n).