Oscillations of Fourier coefficients of product of L-functions at integers in a sparse set

Let f be a normalized Hecke eigenform of weight k for the full modular group [Formula: see text]. In this paper, we obtain the asymptotic of higher moments of general divisor functions associated to the Fourier coefficients of Rankin–Selberg L-functions [Formula: see text], supported at the integers represented by primitive integral positive-definite binary quadratic forms (reduced forms) of a fixed discriminant [Formula: see text]. We improve previous results in the case when the reduced form is given by [Formula: see text].