On a general divisor problem associated to coefficients of Rankin-Selberg L-functions over a sparse set of sequences of positive integers

Let f and g be two distinct normalized primitive holomorphic cusp forms of evenintegral weights k(1 )and k(2 )for the full modular group Gamma=SL(2,Z), respectively.In this paper, we establish the asymptotic formula for the higher power moments ofgeneral divisor problem associated to the coefficients of Rankin-SelbergL-function L(fxg,s), supported at the sequence of positive integers represented by primitive integral positive definite reduced binary quadratic forms of a fixed discriminant D<0.By analogy, we also investigate the similar problem for the coefficients of a certain Rankin-Selberg L-function.